Four carpenters can individually complete a particular task

Question

Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9

Bunuel · Answer

In order three of the carpenters to complete the maximum fraction of the task we should select three fastest carpenters. So, those three who complete the task in 3, 4, and 5 hours.

In 1 hour they will complete  \frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60} th of the task. So, in  \frac{3}{4}  hour (45 minutes) they will complete  \frac{47}{60}*\frac{3}{4}=\frac{47}{80} th of the job.

Answer: D.

Hope it's clear.

pike · Answer

1/3 + 1/4 + 1/5 = 47/60
47/60 * 3/4 = 47 / 80

D

gmatsaga · Answer

Farmer A, B, C, and D

A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour

By intuition we know that the three fastest farmers are A B and C.

As such

(1/3 + 1/4 + 1/5)*(3/4) = ?

47/80 or (D)

Bunuel · Answer

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amanvermagmat · Answer

I sometimes do these by taking total work as number of units which is LCM of individual times. 
LCM of 3,4,5,7 = 420.

Let total work be 420 units. 
Carpenter A does in 1 hour = 420/3 = 140 units.
Carpenter B does in 1 hour = 420/4 = 105 units.
Carpenter C does in 1 hour = 420/5 = 84 units.
Carpenter D does in 1 hour = 420/7 = 60 units.

Clearly, 3 most efficient carpenters are A, B, C. So if we want to find out Max fraction of work possible by 3 carpenters, we have to take these 3 carpenters only. 
They do a total of (140+105+84) = 329 units per hour

Now, 45 minutes = 3/4 hours
Work done in 1 hour = 329 units
Work done in 3/4 hours = 329 * 3/4 = 987/4

Now this is what fraction of total work = (987/4)/420 = 47/80.
Hence  D

(This is a time taking solution for this question no doubt. Method given by others is better. But I am just trying to add some value by giving an alternate solution. This kind of method can be applied to such questions though, sometimes making them easier)

nahid78 · Answer

maximum work will be done by those who take less time to complete the task individually. 
Forty five minutes is 3/4 hour
so ans is 3/4(1/3+1/4+1/5)

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Four carpenters can individually complete a particular task

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Four carpenters can individually complete a particular task

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