Tank fill

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sat Oct 10, 2015 5:03 am

One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

A. 8/15 hr
B. 3/4 hr
C. 5/4 hr
D. 15/8 hr
E. 8/3 hr

Please explain.

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Source: Beat The GMAT — Problem Solving | Sat Oct 10, 2015 5:03 am

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 » Sat Oct 10, 2015 6:06 am

oquiella wrote:One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

A. 8/15 hr
B. 3/4 hr
C. 5/4 hr
D. 15/8 hr
E. 8/3 hr

Let the tank = the LCM of the times in the problem = 5*3 = 15 liters.

Since the slower inlet takes 5 hours to fill the tank, the rate for the slower inlet = w/t = 15/5 = 3 liters per hour.
Since the faster inlet takes 3 hours to fill the tank, the rate for the faster inlet = w/t = 15/3 = 5 liters per hour.
Combined rate for the two inlets working together = 3+5 = 8 liters per hour.

2/3 of the 15-liter tank = (2/3)(15) = 10 liters.
Time for the two inlets together to pump in 10 liters = w/r = 10/8 = 5/4 hours.

The correct answer is C.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Oct 10, 2015 8:58 am

Hi oquiella,

Since we have two 'entities' working on a task together, this is essentially just a Work Formula question. It does come with a minor 'twist' though.

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

The two pipes can fill the tank in 5 hours and 3 hours, respectively. Working together, it would take...

(5)(3)/(5+3) = 15/8 hours to fill the ENTIRE tank.

We're asked how long it would take to fill 2/3 of the tank, so we have to multiply the above number by 2/3...

(15/8)(2/3) = 30/24 = 5/4 hours

Final Answer: C

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Oct 13, 2015 3:09 pm

As the other experts have shown, it's not hard to calculate the answer here. However, when you have two things working together (machines, pipes, robots, etc), we can APPROXIMATE their combined time as follows:

If each inlet pipe filled the tank in 5 hours individually, together they'd fill it in 2.5 hrs.
If each inlet pipe filled the tank in 3 hours individually, together they'd fill it in 1.5 hrs.

Thus, working together, their combined time has to be greater than 1.5 and less than 2.5 hrs. We can estimate that it will take them close to 2 hrs to fill the tank.

If we're asked how long it will take to fill 2/3 of the tank, it will be a number close to 2/3 of 2, or 4/3.

A and B are both less than 1 - eliminate them. E is greater than 2 - eliminate it. D is too close to 2, and C is much closer to 4/3. If you didn't have time to solve and you had to guess, you could narrow it down to C.

Ceilidh Erickson
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Harvard Graduate School of Education

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Oct 14, 2015 10:59 pm

Here's a quick approach:

Work = Rate * Time

Work = (2/3)
Rate = (1/5 + 1/3)
Time = t

so we have

(2/3) = (1/5 + 1/3)t

(2/3) = (8/15)t

(2/3)*(15/8) = t

5/4 = t

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8134; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Feb 15, 2018 10:33 am

oquiella wrote:One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

A. 8/15 hr
B. 3/4 hr
C. 5/4 hr
D. 15/8 hr
E. 8/3 hr

The combined rate of the pipes is 1/5 + 1/3 = 3/15 + 5/15 = 8/15.

If we let n = the time if takes to fill the 2/3 of the tank, then:

(8/15)n = 2/3

Multiplying by 15, we have:

8n = 10

n = 10/8 = 5/4 hours

Answer:C

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