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22 Apr 2020, 06:20
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:44) correct
36%
(03:08)
wrong
based on 183
sessions
History
Date
Time
Result
Not Attempted Yet
Working alone, A needs 4 less hours than B to complete the job. If A and B together can complete the job in 288 minutes, how long does B alone take to complete the job?
A. 6 hr
B. 8 hrs
C. 10 hrs
D. 12 hrs
E. 15 hrs
A. 6 hr
B. 8 hrs
C. 10 hrs
D. 12 hrs
E. 15 hrs
22 Apr 2020, 06:48
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Let the time taken by B be \(x\) hours, then A takes x-4 hours. We are given that both machines when operated together takes 288 minutes = \(\frac{448}{60} = 4\frac{4}{5} = \frac{24}{5}\)\(hrs\) This means that 1 unit of work done by both machines is \(1/(\frac{24}{5}) = \frac{5}{24}\)
Hence \(\frac{1}{x}+\frac{1}{x-4}=\frac{5}{24}\)
Testing using the answer choices. C and E can be eliminated because they are not factors of 24. At least it is best to test with numbers that are factors of 24. Best to look for the answer choice that is such that the LCM of that number and that number minus 4 is 24. So start with \(x=\frac{24}{2}=12\)
\(\frac{1}{12}+\frac{1}{(12-4)}=\frac{1}{12}+\frac{1}{8}=\frac{2+3}{24}=\frac{5}{24}\)
The answer is therefore D.
Hence \(\frac{1}{x}+\frac{1}{x-4}=\frac{5}{24}\)
Testing using the answer choices. C and E can be eliminated because they are not factors of 24. At least it is best to test with numbers that are factors of 24. Best to look for the answer choice that is such that the LCM of that number and that number minus 4 is 24. So start with \(x=\frac{24}{2}=12\)
\(\frac{1}{12}+\frac{1}{(12-4)}=\frac{1}{12}+\frac{1}{8}=\frac{2+3}{24}=\frac{5}{24}\)
The answer is therefore D.
25 Apr 2020, 00:46
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Can somebody please explain the solution of this in detail ??
