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10 Jun 2010, 12:30
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A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7
B) 1/3
C) 2/3
D) 3/4
E) 4/3
A) 4/7
B) 1/3
C) 2/3
D) 3/4
E) 4/3
My solution:
Rate at which the master builder does work: x
Rate at which each apprentice works: (2/3)x
For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3.
Any pointers???
Rate at which the master builder does work: x
Rate at which each apprentice works: (2/3)x
For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3.
Any pointers???
10 Jun 2010, 15:31
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tingle15
Can somebody help me with the following question...
A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7
B) 1/3
C) 2/3
D) 3/4
E) 4/3
My solution:
Rate at which the master builder does work: x
Rate at which each apprentice works: (2/3)x
For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3.
Any pointers???
A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7
B) 1/3
C) 2/3
D) 3/4
E) 4/3
My solution:
Rate at which the master builder does work: x
Rate at which each apprentice works: (2/3)x
For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3.
Any pointers???
Rate of the master - \(x\);
Rate of one apprentice would be \(\frac{2}{3}x\), the rate of the 3 apprentices would be \(3*\frac{2}{3}x=2x\).
Combined rate of the master and 3 apprentices would be \(x+2x=3x\).
The master and 3 apprentices will do the job in \(time_{group}=\frac{job}{rate}=\frac{job}{3x}\);
Only the master will do the job in \(time_{master}=\frac{job}{rate}=\frac{job}{x}\).
So if the master alone needs 3 hours to do the job then the group will need 1 hour to do the job, which is 1/3 of the time needed by the master:
\(\frac{time_{group}}{time_{master}}=\frac{job}{3x}*\frac{x}{job}=\frac{1}{3}\).
Answer: B.
General Discussion
06 Jul 2010, 06:08
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Please tell me whether my approach is right or wrong,
Let the time taken by the master builder be 12 hrs
Then, time taken by each apprentice will be 8 hrs. (since they're each 2/3rd as fast as the mb)
So, total time taken by them to finish the task - 12+8(3) = 36
fracn = 12/36 = 1/3
Let the time taken by the master builder be 12 hrs
Then, time taken by each apprentice will be 8 hrs. (since they're each 2/3rd as fast as the mb)
So, total time taken by them to finish the task - 12+8(3) = 36
fracn = 12/36 = 1/3
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