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Three neighborhood children, individually, can mow Mr. Phelps's lawn i

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Three neighborhood children, individually, can mow Mr. Phelps's lawn i  [#permalink]

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New post 16 Oct 2016, 02:38
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Three neighborhood children, individually, can mow Mr. Phelps's lawn in 1.5, 2, and 3 hours, respectively. What is the fastest the job can be completed by two of the children working together at their respective rates?

a) 6/7 hours
b) 3/2 hours
c) 7/4 hours
d) 7/2 hours
e) 5 hours

Please assist with above problem.
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Re: Three neighborhood children, individually, can mow Mr. Phelps's lawn i  [#permalink]

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New post 16 Oct 2016, 02:45
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alanforde800Maximus wrote:
Three neighborhood children, individually, can mow Mr. Phelps's lawn in 1.5, 2, and 3 hours, respectively. What is the fastest the job can be completed by two of the children working together at their respective rates?

a) 6/7 hours
b) 3/2 hours
c) 7/4 hours
d) 7/2 hours
e) 5 hours

Please assist with above problem.


The fastest children are those who can mow the lawn in 1.5 (3/2) and 2 hours. Their individual rates are 2/3 and 1/2 lawn/hour.

Their combined rate is 2/3 + 1/2 = 7/6 lawn/hour. The time is a reciprocal of the rate, thus working together at their respective rates these two children can mow the lawn in 6/7 hours.

Answer: A.
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Re: Three neighborhood children, individually, can mow Mr. Phelps's lawn i  [#permalink]

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New post 16 Oct 2016, 03:34
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alanforde800Maximus wrote:
Three neighborhood children, individually, can mow Mr. Phelps's lawn in 1.5, 2, and 3 hours, respectively. What is the fastest the job can be completed by two of the children working together at their respective rates?

a) 6/7 hours
b) 3/2 hours
c) 7/4 hours
d) 7/2 hours
e) 5 hours

Please assist with above problem.


Let the total work be 6 units...

Efficiency of child A = 6/1.5 = 4 units/hour
Efficiency of child B = 6/2 = 3 units/hour
Efficiency of child C = 6/3 = 2 units/hour

Quote:
What is the fastest the job can be completed by two of the children working together at their respective rates?


Since the efficiency of child A and Child B are faster than C , their combined efficiency is 7 ( ie, 4 + 3 )

So, Time taken by A and B working at their respective rates is 6/7

Hence correct answer must be (A)

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Re: Three neighborhood children, individually, can mow Mr. Phelps's lawn i  [#permalink]

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New post 26 Jan 2018, 13:33
Hi All,

You can answer this question with 10 seconds of logical thinking and no actual work - and you're not likely to see questions designed in that way on the Official GMAT.

Since the individual times it takes to mow the lawn are 1.5 hours, 2 hours and 3 hours, the fastest child can mow the lawn by himself in 1.5 hours. If he has help, then it would take LESS time than that - there's only one answer that logically fits...

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Re: Three neighborhood children, individually, can mow Mr. Phelps's lawn i   [#permalink] 26 Jan 2018, 13:33
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