rates problem

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rtaha2412: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Fri Nov 27, 2009 7:48 pm; Thanked: 1 times

by rtaha2412 » Mon Jan 03, 2011 5:32 pm

If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

16
12
8.6
5
4.75

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Source: Beat The GMAT — Problem Solving | Mon Jan 03, 2011 5:32 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Mon Jan 03, 2011 5:46 pm

rtaha2412 wrote:If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

16
12
8.6
5
4.75

Rate of cold water tap = 1/400
Rate of hot water tap = 1/480
Rate of drainage = 1/800 (all in sec)

Effective rate = 1/400 + 1/480 - 1/800 = 8/2400 = 1/300
Hence, required time = 300 Sec = 5 mins

D

Thanks
Anshu

(Every mistake is a lesson learned )

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jan 03, 2011 6:21 pm

rtaha2412 wrote:If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

16
12
8.6
5
4.75

Plug in tub = 40 liters.

Time for cold water = 20/3 minutes, so rate for cold water = w/t = 40/(20/3) = 6 liters per minute.
Time for hot water = 8 minutes, so rate for hot water = w/t = 40/8 = 5 liters per minute.
Time for drain = 40/3 minutes, so rate for drain = 40/(40/3) = 3 liters per minute.
Combined rate for all 3 = cold + hot - drain = 6+5-3 = 8 liters per minute.
Time to fill with all 3 running = w/r = 40/8 = 5 minutes.

The correct answer is D.

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