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# Working together, each at his or her own constant rate, Jeff and Ashle

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Math Expert
Joined: 02 Sep 2009
Posts: 58421
Working together, each at his or her own constant rate, Jeff and Ashle  [#permalink]

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05 Mar 2019, 04:28
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Difficulty:

5% (low)

Question Stats:

92% (01:07) correct 8% (01:33) wrong based on 39 sessions

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Working together, each at his or her own constant rate, Jeff and Ashley painted their apartment in 6 hours. Working at his constant rate, Jeff could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley, working at her constant rate, to paint the apartment?

A. 4
B. 12
C. 15
D. 16
E. 20

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Re: Working together, each at his or her own constant rate, Jeff and Ashle  [#permalink]

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05 Mar 2019, 04:48
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Bunuel wrote:
Working together, each at his or her own constant rate, Jeff and Ashley painted their apartment in 6 hours. Working at his constant rate, Jeff could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley, working at her constant rate, to paint the apartment?

A. 4
B. 12
C. 15
D. 16
E. 20

Let, Apartment painting work = 60 units

Hourly work of Jeff and Ashley = 60/6 = 10 units

Hourly work of Jeff = 60/10 = 6 units

i.e. Hourly work of Ashley = 10 - 6 = 4 units

Total Time taken by Ashley to finish 60 unit works = 60/4 = 15 hours

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Re: Working together, each at his or her own constant rate, Jeff and Ashle  [#permalink]

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05 Mar 2019, 05:28
One way to do this question is to Backsolve, or essentially "try out" the answer choices.

Let's say it takes Ashley 15 hours (choosing answer choice (C)). Ashley would have a 1/15 rate and Jeff's rate is 1/10 each hour. Working together they would do 1/15 + 1/10 each hour, or 2/30 + 3/30 = 5/30 = 1/6 in one hour. Then, yes, it does make sense that together the would do the job in 6 hours.

We got lucky here that (C) ended up being the correct answer, but if our answer had not matched the given information, then we probably could have discerned the correct answer based on how "too big" or "too small" we were.

While not required, sometimes we forget how useful leveraging the answer choices can be!
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Re: Working together, each at his or her own constant rate, Jeff and Ashle  [#permalink]

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05 Mar 2019, 11:23
Bunuel wrote:
Working together, each at his or her own constant rate, Jeff and Ashley painted their apartment in 6 hours. Working at his constant rate, Jeff could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley, working at her constant rate, to paint the apartment?

A. 4
B. 12
C. 15
D. 16
E. 20

let time of Jeff= x and Ashley = y
so
given
x+y/xy = 1/6
and x = 10
so solve for y
10+y = 10y/6
or say
60+6y = 10y
y = 15 hrs
IMO C
Re: Working together, each at his or her own constant rate, Jeff and Ashle   [#permalink] 05 Mar 2019, 11:23
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