Manhattan Prep
Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?
A. 5/12 hours
B. 5/8 hours
C. 8/5 hours
D. 12/7 hours
E. 12/5 hours
OA C
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Two hoses are pouring water into an empty pool. Hose 1 alone
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GMATGuruNY
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Let the pool = 12 gallons.AAPL wrote:Manhattan Prep
Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?
A. 5/12 hours
B. 5/8 hours
C. 8/5 hours
D. 12/7 hours
E. 12/5 hours
Since Hose 1 takes 6 hours to fill the 12-gallon pool, the rate for Hose 1 = w/t = 12/6 = 2 gallons per hour.
Since Hose 2 takes 4 hours to fill the 12-gallon pool, the rate for Hose 2 = w/t = 12/4 = 3 gallons per hour.
Since the combined rate for the two hoses = 2+3 = 5 gallons per hour, the time to fill 2/3 of the 12-gallon pool = w/r = (2/3 * 12)/5 = 8/5 hours.
The correct answer is C.
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Scott@TargetTestPrep
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We see that the rate of hose 1 is 1/6, and the rate of hose 2 is 1/4. We can let x = time needed to fill 2/3 of a pool when they work together and create the equation:AAPL wrote:Manhattan Prep
Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?
A. 5/12 hours
B. 5/8 hours
C. 8/5 hours
D. 12/7 hours
E. 12/5 hours
OA C
1/6(x) + 1/4(x) = 2/3
Multiplying the equation by 12, we have:
2x + 3x = 8
5x = 8
x = 8/5 hours
Answer: C
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Hi All,
This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.
Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.
Here, we're told that Hose 1 can fill a pool in 6 hours and that Hose 2 can fill the pool in 4 hours. We're asked how long it takes the two hoses to fill 2/3 of the pool...
To fill the ENTIRE POOL, it takes...
(6)(4)/(6+4) = 24/10 = 2.4 hours
To fill 2/3 of the pool takes 2/3 of the time. Since 2.4 hours = 12/5 hours, it would take...
(2/3)(12/5) = 24/15 = 8/5 hours to fill 2/3 of the pool.
Final Answer: C
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This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.
Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.
Here, we're told that Hose 1 can fill a pool in 6 hours and that Hose 2 can fill the pool in 4 hours. We're asked how long it takes the two hoses to fill 2/3 of the pool...
To fill the ENTIRE POOL, it takes...
(6)(4)/(6+4) = 24/10 = 2.4 hours
To fill 2/3 of the pool takes 2/3 of the time. Since 2.4 hours = 12/5 hours, it would take...
(2/3)(12/5) = 24/15 = 8/5 hours to fill 2/3 of the pool.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
