An outlet pipe empties a tank in 5

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

An outlet pipe empties a tank in 5

by BTGmoderatorDC » Sat Nov 04, 2017 4:14 am

An outlet pipe empties a tank in 5 hours when the tank is 50% full. An inlet pipe, which lets water in at 1/3 liters per min, is opened when the tank was empty and it took 10 hours to fill the tank completely.

Find the capacity of the tank.

A. 10 liters.

B. 100 liters.

C. 1000 liters.

D. 500 liters.

E. 200 liters.

I'm quite confuse on how to solve this, can some experts help?

OA B

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Source: Beat The GMAT — Problem Solving | Sat Nov 04, 2017 4:14 am

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by [email protected] » Sat Nov 04, 2017 11:53 am

Hi lheiannie07,

We're told that an outlet pipe empties a tank in 5 hours when the tank is 50% full and that an inlet pipe lets water in at 1/3 liters per min. We're told that the tank starts off empty and took 10 hours to fill the tank. We're asked for the capacity of the tank.

Although the prompt does not state it, we're meant to assume that both pipes are 'working' at the same time. This question gives us two rates, but provides the information in different units. Thus, we have to 'modify' the given information a bit:

Inlet Pipe = 1/3 liters/min = (60 mins)(1/3 liter/min) = 20 liters/hour
Outlet Pipe = 5 hours to remove HALF the tank = (1/2 tank)/5 hours = 1/10 of the tank is emptied per hour

Since it take 10 hours to fill the tank, we have...
(20 liters)(10 hours) = 200 liters going IN
(1/10 tank)(10 hours) = 1 "full tank" going OUT

In algebraic terms, that would be: 200 - X = X
X = 100 liters

Final Answer: B

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Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Thu Oct 31, 2019 5:23 pm

BTGmoderatorDC wrote:An outlet pipe empties a tank in 5 hours when the tank is 50% full. An inlet pipe, which lets water in at 1/3 liters per min, is opened when the tank was empty and it took 10 hours to fill the tank completely.

Find the capacity of the tank.

A. 10 liters.

B. 100 liters.

C. 1000 liters.

D. 500 liters.

E. 200 liters.

I'm quite confuse on how to solve this, can some experts help?

OA B

We can let c = the full capacity of the tank, in liters. If the outlet pipe empties the tank in 5 hours when the tank is 50% full, then it will empty the tank in 10 hours when the tank is 100% full. Therefore, the rate of the outlet pipe c/10 liters per hour.

Since the inlet pipe has a rate of 1/3 liters per minute, its rate is 1/3 x 60 = 20 liters per hour. Since it took 10 hours to fill the tank completely (while the outlet pipe is open), we can create the equation:

10(20 - c/10) = c

200 - c = c

200 = 2c

100 = c

Answer: B

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