← Net fill rate is inflow minus outflow · Track a Quantity Through Changes

Net fill rate is inflow minus outflow · 10 practice problems

3.MD.A.23.OA.A.3

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 8 seconds

A faucet pours $10\ \text{fl oz}$ of water each second into an empty bucket that holds $64\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $2\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 10 fl oz of water each second to an empty bucket that holds 64 fl oz, but a hole lets 2 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 10 fl oz per second.
Water leaks out at 2 fl oz per second.
The bucket holds 64 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 10 fl oz come in and 2 fl oz leak out, so the water level rises by 10 - 2 = 8 fl oz each second.

10 - 2 = 8\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 64 fl oz and fills 8 fl oz each second, so the time is 64 divided by 8, which is 8 seconds.

64 \div 8 = 8\ \text{seconds}

Filling 8 fl oz each second, it takes 8 equal seconds to reach 64 fl oz.

Answer: 8 seconds

4 · Reviewdoes it hold up?

At 8 fl oz per second for 8 seconds we get 8 x 8 = 64 fl oz, exactly the bucket's capacity, so 8 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 8, 16, 24, 32, 40, 48, 56, 64 fl oz, reaching full at the 8th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 10 minus 2 = 8 fl oz!

Variant 2 easy answer: 6 seconds

A faucet pours $22\ \text{fl oz}$ of water each second into an empty bucket that holds $90\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $7\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 22 fl oz of water each second to an empty bucket that holds 90 fl oz, but a hole lets 7 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 22 fl oz per second.
Water leaks out at 7 fl oz per second.
The bucket holds 90 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 22 fl oz come in and 7 fl oz leak out, so the water level rises by 22 - 7 = 15 fl oz each second.

22 - 7 = 15\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 90 fl oz and fills 15 fl oz each second, so the time is 90 divided by 15, which is 6 seconds.

90 \div 15 = 6\ \text{seconds}

Filling 15 fl oz each second, it takes 6 equal seconds to reach 90 fl oz.

Answer: 6 seconds

4 · Reviewdoes it hold up?

At 15 fl oz per second for 6 seconds we get 15 x 6 = 90 fl oz, exactly the bucket's capacity, so 6 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 15, 30, 45, 60, 75, 90 fl oz, reaching full at the 6th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 22 minus 7 = 15 fl oz!

Variant 3 easy answer: 6 seconds

A faucet pours $18\ \text{fl oz}$ of water each second into an empty bucket that holds $90\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $3\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 18 fl oz of water each second to an empty bucket that holds 90 fl oz, but a hole lets 3 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 18 fl oz per second.
Water leaks out at 3 fl oz per second.
The bucket holds 90 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 18 fl oz come in and 3 fl oz leak out, so the water level rises by 18 - 3 = 15 fl oz each second.

18 - 3 = 15\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 90 fl oz and fills 15 fl oz each second, so the time is 90 divided by 15, which is 6 seconds.

90 \div 15 = 6\ \text{seconds}

Filling 15 fl oz each second, it takes 6 equal seconds to reach 90 fl oz.

Answer: 6 seconds

4 · Reviewdoes it hold up?

At 15 fl oz per second for 6 seconds we get 15 x 6 = 90 fl oz, exactly the bucket's capacity, so 6 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 15, 30, 45, 60, 75, 90 fl oz, reaching full at the 6th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 18 minus 3 = 15 fl oz!

Variant 4 medium answer: 8 seconds

A faucet pours $14\ \text{fl oz}$ of water each second into an empty bucket that holds $96\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $2\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 14 fl oz of water each second to an empty bucket that holds 96 fl oz, but a hole lets 2 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 14 fl oz per second.
Water leaks out at 2 fl oz per second.
The bucket holds 96 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 14 fl oz come in and 2 fl oz leak out, so the water level rises by 14 - 2 = 12 fl oz each second.

14 - 2 = 12\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 96 fl oz and fills 12 fl oz each second, so the time is 96 divided by 12, which is 8 seconds.

96 \div 12 = 8\ \text{seconds}

Filling 12 fl oz each second, it takes 8 equal seconds to reach 96 fl oz.

Answer: 8 seconds

4 · Reviewdoes it hold up?

At 12 fl oz per second for 8 seconds we get 12 x 8 = 96 fl oz, exactly the bucket's capacity, so 8 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 12, 24, 36, 48, 60, 72, 84, 96 fl oz, reaching full at the 8th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 14 minus 2 = 12 fl oz!

Variant 5 medium answer: 12 seconds

A faucet pours $12\ \text{fl oz}$ of water each second into an empty bucket that holds $96\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $4\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 12 fl oz of water each second to an empty bucket that holds 96 fl oz, but a hole lets 4 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 12 fl oz per second.
Water leaks out at 4 fl oz per second.
The bucket holds 96 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 12 fl oz come in and 4 fl oz leak out, so the water level rises by 12 - 4 = 8 fl oz each second.

12 - 4 = 8\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 96 fl oz and fills 8 fl oz each second, so the time is 96 divided by 8, which is 12 seconds.

96 \div 8 = 12\ \text{seconds}

Filling 8 fl oz each second, it takes 12 equal seconds to reach 96 fl oz.

Answer: 12 seconds

4 · Reviewdoes it hold up?

At 8 fl oz per second for 12 seconds we get 8 x 12 = 96 fl oz, exactly the bucket's capacity, so 12 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 fl oz, reaching full at the 12th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 12 minus 4 = 8 fl oz!

Variant 6 hard answer: 10 seconds

A faucet pours $16\ \text{fl oz}$ of water each second into an empty bucket that holds $100\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $6\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 16 fl oz of water each second to an empty bucket that holds 100 fl oz, but a hole lets 6 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 16 fl oz per second.
Water leaks out at 6 fl oz per second.
The bucket holds 100 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 16 fl oz come in and 6 fl oz leak out, so the water level rises by 16 - 6 = 10 fl oz each second.

16 - 6 = 10\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 100 fl oz and fills 10 fl oz each second, so the time is 100 divided by 10, which is 10 seconds.

100 \div 10 = 10\ \text{seconds}

Filling 10 fl oz each second, it takes 10 equal seconds to reach 100 fl oz.

Answer: 10 seconds

4 · Reviewdoes it hold up?

At 10 fl oz per second for 10 seconds we get 10 x 10 = 100 fl oz, exactly the bucket's capacity, so 10 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 fl oz, reaching full at the 10th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 16 minus 6 = 10 fl oz!

Variant 7 medium answer: 5 seconds

A faucet pours $25\ \text{fl oz}$ of water each second into an empty bucket that holds $100\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $5\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 25 fl oz of water each second to an empty bucket that holds 100 fl oz, but a hole lets 5 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 25 fl oz per second.
Water leaks out at 5 fl oz per second.
The bucket holds 100 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 25 fl oz come in and 5 fl oz leak out, so the water level rises by 25 - 5 = 20 fl oz each second.

25 - 5 = 20\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 100 fl oz and fills 20 fl oz each second, so the time is 100 divided by 20, which is 5 seconds.

100 \div 20 = 5\ \text{seconds}

Filling 20 fl oz each second, it takes 5 equal seconds to reach 100 fl oz.

Answer: 5 seconds

4 · Reviewdoes it hold up?

At 20 fl oz per second for 5 seconds we get 20 x 5 = 100 fl oz, exactly the bucket's capacity, so 5 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 20, 40, 60, 80, 100 fl oz, reaching full at the 5th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 25 minus 5 = 20 fl oz!

Variant 8 medium answer: 10 seconds

A faucet pours $15\ \text{fl oz}$ of water each second into an empty bucket that holds $100\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $5\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 15 fl oz of water each second to an empty bucket that holds 100 fl oz, but a hole lets 5 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 15 fl oz per second.
Water leaks out at 5 fl oz per second.
The bucket holds 100 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 15 fl oz come in and 5 fl oz leak out, so the water level rises by 15 - 5 = 10 fl oz each second.

15 - 5 = 10\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 100 fl oz and fills 10 fl oz each second, so the time is 100 divided by 10, which is 10 seconds.

100 \div 10 = 10\ \text{seconds}

Filling 10 fl oz each second, it takes 10 equal seconds to reach 100 fl oz.

Answer: 10 seconds

4 · Reviewdoes it hold up?

At 10 fl oz per second for 10 seconds we get 10 x 10 = 100 fl oz, exactly the bucket's capacity, so 10 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 fl oz, reaching full at the 10th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 15 minus 5 = 10 fl oz!

Variant 9 hard answer: 6 seconds

A faucet pours $30\ \text{fl oz}$ of water each second into an empty bucket that holds $120\ \text{fl oz}$ . But the bucket has a hole, and water leaks out at $10\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 30 fl oz of water each second to an empty bucket that holds 120 fl oz, but a hole lets 10 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 30 fl oz per second.
Water leaks out at 10 fl oz per second.
The bucket holds 120 fl oz.
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 30 fl oz come in and 10 fl oz leak out, so the water level rises by 30 - 10 = 20 fl oz each second.

30 - 10 = 20\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 120 fl oz and fills 20 fl oz each second, so the time is 120 divided by 20, which is 6 seconds.

120 \div 20 = 6\ \text{seconds}

Filling 20 fl oz each second, it takes 6 equal seconds to reach 120 fl oz.

Answer: 6 seconds

4 · Reviewdoes it hold up?

At 20 fl oz per second for 6 seconds we get 20 x 6 = 120 fl oz, exactly the bucket's capacity, so 6 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 20, 40, 60, 80, 100, 120 fl oz, reaching full at the 6th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 30 minus 10 = 20 fl oz!

Variant 10 hard answer: 8 seconds

A faucet pours $20\ \text{fl oz}$ of water each second into an empty bucket that holds $1\ \text{gallon}$ ( $128\ \text{fl oz}$ ). But the bucket has a hole, and water leaks out at $4\ \text{fl oz}$ each second. How many seconds does it take to fill the bucket completely?

Show solution

1 · Understandwhat's really being asked

A faucet adds 20 fl oz of water each second to an empty bucket that holds 128 fl oz (1 gallon), but a hole lets 4 fl oz leak out each second. Find how many seconds it takes to fill the bucket.

Givens

Water pours in at 20 fl oz per second.
Water leaks out at 4 fl oz per second.
The bucket holds 128 fl oz (1 gallon).
The bucket starts empty.

Unknowns

The number of seconds to fill the bucket completely.

Constraints

Inflow and leak happen at the same time, every second.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #5 Look for a Pattern

Each second the bucket gains (inflow minus leak) fluid ounces. Find that net rate, then divide the bucket's capacity by the net rate to get the time.

3 · Execute2 carry out the plan

1Find the net amount added each second

#8 Analyze the Units 3.MD.A.2

In one second, 20 fl oz come in and 4 fl oz leak out, so the water level rises by 20 - 4 = 16 fl oz each second.

20 - 4 = 16\ \text{fl oz per second}

Only the leftover after the leak actually stays in the bucket.

2Divide the capacity by the net rate

#5 Look for a Pattern 3.OA.A.3

The bucket holds 128 fl oz and fills 16 fl oz each second, so the time is 128 divided by 16, which is 8 seconds.

128 \div 16 = 8\ \text{seconds}

Filling 16 fl oz each second, it takes 8 equal seconds to reach 128 fl oz.

Answer: 8 seconds

4 · Reviewdoes it hold up?

At 16 fl oz per second for 8 seconds we get 16 x 8 = 128 fl oz, exactly the bucket's capacity, so 8 seconds is correct.

Another way: Make a systematic list (tool 2): after each second the water is 16, 32, 48, 64, 80, 96, 112, 128 fl oz, reaching full at the 8th second.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Working with fluid-ounce volumes flowing in and out each second.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the capacity by the net fill rate to find the time.

💡Takeaway. This only needs Grade 3 division once you see each second really adds 20 minus 4 = 16 fl oz!