Net fill rate is inflow minus outflow

3.MD.A.23.OA.A.3 · adapt · grade 3

Archetype: Track a Quantity Through Changes · step in a 7-type progression

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

Understand

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.

Plan

#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.

Execute

#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.

#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

Review

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.

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.

Standards · min 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.

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