Here are the answer and explanation to yesterday’s practice question. Thanks for sending in all of your answers!

## The answer:

## Explanation:

### METHOD ONE: Algebraic approach

This approach to this question involves some tricky algebra.

Pump A works at a rate of 1/A and pump B, at a rate of 1/B (these rates are given in units of “pools/minute”). For the time they are working together, we add rates. That’s a HUGE idea in work problems – when two machines or people work together, we add the rates.

In the first minute, pump A works alone and drains an amount of 1/A (that is, one “A-th” of a pool). This leaves an amount of

The time it will take the two pumps, working at the combined rate, to drain this, is:

That’s the time from when the two pumps start working together, which is 1 minute after pump A starts. To get the total time, we need to add 1 to this (this is the trickiest algebra in the whole problem!)

### METHOD TWO: Numerical approach

Let’s say that Pump A can drain a pool in A = 6 minutes, and pump B can drain a pool in B = 3.

Pump A works for a minute, draining 1/6 of the pool, and leaving 5/6 of the pool left.

Then pump B kicks in — A & B work at the combined rate of 1/6 + 1/3 = 1/2. How long does it take the two pumps, working at a rate of 1/2, to drain 5/6 of a pool?

I feel like this guy does a good job with the easy and medium level questions, but he seems to be a bit too robotic on more difficult topics, at least for me. Some of the more obvious steps are skipped over and the entire solution is somewhat hurried. I appreciate the content but from time to time I have this issue with Magoosh.

This explanation can be tough to grasp.. there are plenty of ways to solve these kind of problems ..

Where are the 1’s coming from in this solution?

In addition, how does 1/A –> (A-1)/A? Is A being used as distance or work?

(A – 1)/A = A/A – 1/A = 1 – 1/A. After one minute 1/A has been pumped out. The 1 stands for the total job. So in 1 minute 1 – 1/A of the job remains uncompleted. A in this case stands for work rate.