Video Explanation

Text Explanation

Pump A can empty a pool in 3 hours. That means that it can empty  of a pool in 1 hour. After 3 hours, all three thirds will be empty, so the pool is empty :) Pump B can empty that pool in 2 hours, which means after 1 hour  of the pool will be empty. We can summarize these rates:

To find how long it will take the empty the pool together, we just add the rates. Pump A is working while Pump B is working, so that's:

If you aren’t sure how we got from  to , please read the FAQ below! 

So we know they empty 1 pool in  f an hour, which is 72 minutes. The answer is (A).

Frequently Asked Questions

FAQ: Why did we change  to ?

A: We did this because there’s a special rule that applies to work rate problems. The rule says that if we have a fraction , where x is the amount of work done, and y is the amount of time it takes to do the amount of work, we can flip the fraction upside down to get the amount of time it takes to do one unit of work. 

In this problem, we know that Pump A can empty one pool in 3 hours, and Pump B can empty 1 pool in 2 hours. So we have:

Pump A = 

Pump B = 

So together, they can work at the following rate:

So the fraction  actually represents the amount of work done (5 pools) in a corresponding time period (6 hours). 

Since we have a fraction where the numerator is the amount of work done and the denominator is time, we can flip the fraction upside down to find out how long it takes to do 1 unit of work (i.e. empty 1 pool). 

So the answer is  hours.

FAQ: I don’t like the rule you used to change  to . Can we solve the problem without using that rule? 

A: Yes, we can! 

From the work we did above (in the first FAQ), we know that together, the two pumps can work at the following rate:

Now, we want to change this fraction so the top represents 1 pool. So we’ll multiply both the top and bottom by :

So the two pumps working together can empty 1 pool in  hours.