Operations & Word Problems

Problem

Net fill rate is inflow minus outflow

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.
Measurement & dataOperations
Your answer
seconds
How to solve
Strategy Analyze the Units — 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.
1STEP 1

Find the net amount added each second

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 fl oz per second
2STEP 2

Divide the capacity by the net rate

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 ÷ 16 = 8 seconds
Answer
8 seconds
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.
Takeaway

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

  • Find the net amount added each second
  • Divide the capacity by the net rate
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