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# Four carpenters can individually complete a particular task

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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

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)
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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)
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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

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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