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vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

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by vaibhav101 » Sun Jun 03, 2018 9:32 am

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a tap can fill a tank in 6hrs. After half the tank is filled, 3 more similar taps are opened. What is the total time taken to fill the tank?

A 3hrs 15min
B 3hrs 45min
C 4hrs
D 4hrs 15 min
E 4hrs 45min

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Source: Beat The GMAT — Problem Solving | Sun Jun 03, 2018 9:32 am

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

by GMATGuruNY » Sun Jun 03, 2018 10:56 am

vaibhav101 wrote:a tap can fill a tank in 6hrs. After half the tank is filled, 3 more similar taps are opened. What is the total time taken to fill the tank?

A 3hrs 15min
B 3hrs 45min
C 4hrs
D 4hrs 15 min
E 4hrs 45min

Let the tank = 6 liters.
Since one tap takes 6 hours to fill the 6-liter tank, the rate for each tap = w/t = 6/6 = 1 liter per hour.
Time for one tap to fill half the 6-liter tank = w/r = 3/1 = 3 hours.
After 3 additional taps are opened, the combined rate for 4 taps = 4 liters per hour.
Time for the 4 taps to fill the remaining half of the tank = w/r = 3/4 hour.
Total time to fill the tank = 3 hours + 3/4 hour = 3 hours, 45 minutes.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jun 05, 2018 9:40 am

vaibhav101 wrote:a tap can fill a tank in 6hrs. After half the tank is filled, 3 more similar taps are opened. What is the total time taken to fill the tank?

A 3hrs 15min
B 3hrs 45min
C 4hrs
D 4hrs 15 min
E 4hrs 45min

Since one tap can fill a tank in 6 hours, it can fill half the tank in 3 hours.

After 3 more taps joins in, the rate of 4 taps is 4 x 1/6 = 4/6 = 2/3.

Thus, the time it will take 4 taps to fill the remaining half of the tank is (1/2)/(2/3) = 3/4 hours, or 45 minutes.

So the total time is 3 hours and 45 minutes.

Answer: B

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