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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Sat Oct 06, 2018 2:13 pm

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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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Source: Beat The GMAT — Problem Solving | Sat Oct 06, 2018 2:13 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sun Oct 07, 2018 11:15 am

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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by [email protected] » Sun Oct 07, 2018 2:49 pm

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 [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 13, 2018 5:20 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]