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05 May 2025, 11:10
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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100% (01:34) correct
0% (00:00) wrong based on 1 sessions
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A hose, working alone, is capable of filling up an empty pool in 6 hours. A second hose, working alone, is capable of filling up the empty pool in 4 hours. How long would it take for both hoses together to fill two-thirds of the pool?
05 May 2025, 19:33
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A hose, working alone, is capable of filling up an empty pool in 6 hours
◉ Rate of First Hose = X
◉ Let work done = 1
Using Rate * Time = Work Done
X * 6 = 1
=> X = \(\frac{1}{6}\)
A second hose, working alone, is capable of filling up the empty pool in 4 hours.
◉ Rate of Second Hose = Y
◉ Work done = 1
Using Rate * Time = Work Done
Y * 4 = 1
=> Y = \(\frac{1}{4}\)
How long would it take for both hoses together to fill two-thirds of the pool?
◉ Combined Rate = X + Y = \(\frac{1}{6}\) + \(\frac{1}{4}\) = \(\frac{10}{24}\) = \(\frac{5}{12}\)
◉ Work done = \(\frac{2}{3}\)
Using Rate * Time = Work Done
\(\frac{5}{12}\) * Time = \(\frac{2}{3}\)
=> Time = \(\frac{2 * 12}{3 * 5}\) = \(\frac{8}{5}\)
=> Time = 1 + \(\frac{3}{5}\) hours = 1 hour + \(\frac{3 * 60}{5}\) mins = 1 hour 36 mins
So, Answer will be \(\frac{8}{5}\) or 1 hour 36 mins
Hope it helps!
Watch following video to MASTER Work Rate Problems
◉ Rate of First Hose = X
◉ Let work done = 1
Using Rate * Time = Work Done
X * 6 = 1
=> X = \(\frac{1}{6}\)
A second hose, working alone, is capable of filling up the empty pool in 4 hours.
◉ Rate of Second Hose = Y
◉ Work done = 1
Using Rate * Time = Work Done
Y * 4 = 1
=> Y = \(\frac{1}{4}\)
How long would it take for both hoses together to fill two-thirds of the pool?
◉ Combined Rate = X + Y = \(\frac{1}{6}\) + \(\frac{1}{4}\) = \(\frac{10}{24}\) = \(\frac{5}{12}\)
◉ Work done = \(\frac{2}{3}\)
Using Rate * Time = Work Done
\(\frac{5}{12}\) * Time = \(\frac{2}{3}\)
=> Time = \(\frac{2 * 12}{3 * 5}\) = \(\frac{8}{5}\)
=> Time = 1 + \(\frac{3}{5}\) hours = 1 hour + \(\frac{3 * 60}{5}\) mins = 1 hour 36 mins
So, Answer will be \(\frac{8}{5}\) or 1 hour 36 mins
Hope it helps!
Watch following video to MASTER Work Rate Problems
18 May 2025, 00:47
Kudos
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OE
Since Hose 1 can fill the pool in 6 hours, its rate is image pool per hour. Likewise, since Hose 2 can fill the pool in 4 hours, its rate is image pool per hour. Add the two rates to find the combined rate.
\(\frac{6}{1}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{5}{12}\)
In the question, the pool is filled to two-thirds of its capacity. Use the rate and work to find the time.
It will take \(\frac{8}{5}\) of an hour. The real test could also put the answer choice in the form 1 hour 36 minutes or \(1\frac{3}{5}\) of an hour.
GMAT-Club-Forum-6nxjj32g.png [ 27.73 KiB | Viewed 177 times ]
Since Hose 1 can fill the pool in 6 hours, its rate is image pool per hour. Likewise, since Hose 2 can fill the pool in 4 hours, its rate is image pool per hour. Add the two rates to find the combined rate.
\(\frac{6}{1}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{5}{12}\)
In the question, the pool is filled to two-thirds of its capacity. Use the rate and work to find the time.
It will take \(\frac{8}{5}\) of an hour. The real test could also put the answer choice in the form 1 hour 36 minutes or \(1\frac{3}{5}\) of an hour.
Attachment:
GMAT-Club-Forum-6nxjj32g.png [ 27.73 KiB | Viewed 177 times ]
