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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Tank fill
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GMATGuruNY
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Let the tank = the LCM of the times in the problem = 5*3 = 15 liters.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
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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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
GMAT assassins aren't born, they're made,
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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
GMAT assassins aren't born, they're made,
Rich
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ceilidh.erickson
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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.
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Matt@VeritasPrep
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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
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
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The combined rate of the pipes is 1/5 + 1/3 = 3/15 + 5/15 = 8/15.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
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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