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GRE Math Work Rate: Practice Question of the Week #29 Answer

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

The answer:



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.

algebraic approach

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

algebraic approach

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

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!)
algebraic approach

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?

numerical approach

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4 Responses to GRE Math Work Rate: Practice Question of the Week #29 Answer

  1. Jared Hensley July 30, 2014 at 12:27 pm #

    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.

  2. Piyush Chaudhary June 14, 2014 at 10:46 am #

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

  3. Arnita December 14, 2011 at 2:26 pm #

    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?

    • Chris Lele
      Chris December 14, 2011 at 5:13 pm #

      (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.

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