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22 Apr 2020, 04:52
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B
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Difficulty:
55%
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Question Stats:
71% (02:48) correct
29%
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wrong
based on 171
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Working alone, B takes 12 more hours than A to complete a certain job. If they work together, they take 16 fewer hours than B would take to complete the job. How long will it take A and B together to complete the job?
A. 6 hrs
B. 8 hrs
C. 10 hrs
D. 12 hrs
E. 16 hrs
Are You Up For the Challenge: 700 Level Questions
A. 6 hrs
B. 8 hrs
C. 10 hrs
D. 12 hrs
E. 16 hrs
Are You Up For the Challenge: 700 Level Questions
22 Apr 2020, 05:36
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Let \(x\) be the time taken by A to complete the work. Then B takes \(x+12\) hours. If they work together it would take them \((x+12)-16=x-4\) hours. We are to determine \(x-4\)
\(\frac{1}{x}+\frac{1}{x+12}=\frac{1}{x-4}\)
\(\frac{2x+12}{x^2+12x}=\frac{1}{x-4}\)
\((2x+12)(x-4)=x^2+12x\)
\(2x^2+4x-48=x^2+12x\)
\(x^2-8x-48=0\)
\((x-12)(x+4)=0\)
\(x=12\)
\(x-4=8\)
The answer is B.
\(\frac{1}{x}+\frac{1}{x+12}=\frac{1}{x-4}\)
\(\frac{2x+12}{x^2+12x}=\frac{1}{x-4}\)
\((2x+12)(x-4)=x^2+12x\)
\(2x^2+4x-48=x^2+12x\)
\(x^2-8x-48=0\)
\((x-12)(x+4)=0\)
\(x=12\)
\(x-4=8\)
The answer is B.
22 Apr 2020, 05:43
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Bunuel
Use the choices..
Let us start with C...
So A and B do the work together in 10 hrs, B will take 10+16=26hrs and A in 26-12=14 hrs..
The numbers 26 and 14 should tell you that, you cannot get 10 from it.....
\(\frac{1}{26}+\frac{1}{14}=\frac{26+14}{26*14}\neq{\frac{1}{6}}\)
Let us try B..
So A and B do the work together in 8 hrs, B will take 8+16=24hrs and A in 24-12=12 hrs..
The numbers 24 and 12 should can give you an integer as answer.....
\(\frac{1}{24}+\frac{1}{12}=\frac{24+12}{24*12}=\frac{36}{8*3*12}={\frac{1}{8}}\)
B
