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07 May 2017, 13:47
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C
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Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?
A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes
A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes
08 May 2017, 04:22
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Let time taken by Ali = x hours
time taken by Moe= 5x hours
Work done by both of them in 1 hour:
\(\frac{1}{x}\) + \(\frac{1}{5x}\)= \(\frac{1}{4}\)
\(\frac{5 +1}{5x}\) =\(\frac{1}{4}\)
\(\frac{6}{5x}\)= \(\frac{1}{4}\); x= \(\frac{24}{5}\); x= 4\(\frac{4}{5}\) or 4 hour 48 mins
Thus, Time taken by Ali= 4 hours 48 mins.
Answer: C.
Kudos please if you like my explanation!
time taken by Moe= 5x hours
Work done by both of them in 1 hour:
\(\frac{1}{x}\) + \(\frac{1}{5x}\)= \(\frac{1}{4}\)
\(\frac{5 +1}{5x}\) =\(\frac{1}{4}\)
\(\frac{6}{5x}\)= \(\frac{1}{4}\); x= \(\frac{24}{5}\); x= 4\(\frac{4}{5}\) or 4 hour 48 mins
Thus, Time taken by Ali= 4 hours 48 mins.
Answer: C.
Kudos please if you like my explanation!
General Discussion
Updated on: 07 May 2017, 20:48
Originally posted by quantumliner on 07 May 2017, 15:00.
Last edited by quantumliner on 07 May 2017, 20:48, edited 1 time in total.
Last edited by quantumliner on 07 May 2017, 20:48, edited 1 time in total.
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Rate at which Ali works = 1/a
Rate at which Moe works = 1/m
(1/a + 1/m) * 4 = 1
1/a = 5 * 1/m
(1/a + 1/5a) * 4 = 1
6*4/5a = 1
a = 24/5 hours = 4.8 hours = 4 hours 48 minutes
Answer is C. 4 hours 48 minutes
Rate at which Moe works = 1/m
(1/a + 1/m) * 4 = 1
1/a = 5 * 1/m
(1/a + 1/5a) * 4 = 1
6*4/5a = 1
a = 24/5 hours = 4.8 hours = 4 hours 48 minutes
Answer is C. 4 hours 48 minutes
