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Working alone, pump A can empty a pool in 3 hours. Working

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Working alone, pump A can empty a pool in 3 hours. Working

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Source: Magoosh

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

The OA is A.

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Hi All,

We're told that working alone, Pump A can empty a pool in 3 HOURS and Pump B can empty the same pool in 2 HOURS. We're asked how many MINUTES it would take the two pumps, working together, to empty the pool. This question can be solved in a couple of different ways, including with the Work Formula:

Work = (A)(B)/(A+B) where A and B are the 2 individual times it takes to complete the task

Since Pump A can empty the pool in 3 hours and Pump B can empty the pool in 2 hours, it would take (3)(2)/(3+2) = 6/5 to drain the pool. Since 1/5 of an hour is 12 minutes, the total time would be 60 + 12 = 72 minutes to empty the pool.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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If pump A can empty pool in 3 hours
$$In\ 1\ hour\ it\ will\ empty\ \frac{1}{3}of\ the\ pool$$
If pump B can empty the pool in 2 hours,
$$In\ 1\ hour\ it\ will\ empty\ \frac{1}{2}of\ the\ pool$$
By working together their work rate per hour =
$$=\ \frac{1}{3}+\frac{1}{2}$$
$$=\frac{\left(2+3\right)}{6}=\ \frac{5}{6}of\ the\ pool\ per\ hour$$
1 hour = 60 minutes.
$$If\ the\ two\ pumps\ can\ empty\ \frac{5}{6}of\ the\ pool\ in\ 60\ \min utes,\ how\ many\ \min utes\ will\ it\ take\ for\ them\ to\ empty\ the\ whole\ pool\ completely.$$
$$\frac{5}{6}=60\ \min utes$$
$$1\ =\ x$$
$$\frac{5}{6}x\ =60\ \cdot\ 1$$
$$x\ =\ \frac{60}{\frac{5}{6}}$$
$$x=\frac{60\cdot6}{5}\ =\ \frac{360}{5}=72$$
Option A is CORRECT.

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BTGmoderatorLU wrote:
Source: Magoosh

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108
The combined rate of pumps A and B is:

1/3 + 1/2 = 2/6 + 3/6 = 5/6, so the time is 1/(5/6) = 6/5 hours, which is 6/5 x 60 = 72 minutes.

Answer: A

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Scott Woodbury-Stewart Founder and CEO

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