Problem: Two pumps were required to pump the water out of a submerged area after a flood. Pump A, the larger of the two pumps, can pump the water out in 24 hours, whereas it would take pump B 120 hours. Both pumps were working for the first 8 hours until pump A broke down. How long did it take pump B to pump the remaining water?
Solution:
Create a table. List each individual and the time it takes to complete the job. Also include a row for the pumps working together. Use a variable to represent the unknown time to complete the job when the pumps are working together.
| 24 hours | ||
| 120 hours | ||
| Together | x |
Fill in the table with the portion of the job completed in one hour.
If it takes Pump A 24 hours to complete the whole job, one twenty-forth (1/24) of the job will be completed in one hour.
If it takes Pump B 120 hours to complete the whole job, one one hundred twentieth (1/120) of the job will be completed in one hour.
If it takes x number of hours when the pumps are working together 1/x portion of the job will be completed in one hour.
| Portion completed in 1 hour | ||
| 24 hours | 1/24 | |
| 120 hours | 1/120 | |
| Together | x | 1/x |
From here an equation can be created with the portion of the job completed in one hour.
In one hour, the portion completed by pump A plus the portion completed by pump B should equal the portion when they are working together.
Solve the equation to find x.
| The original equation is a rational equation. | |
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| Solve the remaining linear equation. |    |
It would take both pumps working together 20 hours to pump out all of the water.
But the two pumps are only working together for 8 hours which means they only get eight-twentieths (8/20) of the job done. This fraction reduces to two-fifths (2/5).
Three-fifths (3/5) of the water remains and pump B is working alone.
It takes pump B 120 hours to complete the whole job. It will take 120(3/5) to pump the remaining water out.
120(3/5)= 72 hours.
It takes pump B 72 hours to pump the remaining water.