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# It takes Avery 3 hours to build a brick wall while Tom can do it in 2.

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Math Expert
Joined: 02 Sep 2009
Posts: 49913
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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27 Jun 2016, 04:07
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:13) correct 27% (02:22) wrong based on 204 sessions

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It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

A. 25 minutes.
B. 30 minutes.
C. 40 minutes.
D. 55 minutes.
E. 1 hour and 20 minutes.

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Director
Joined: 20 Feb 2015
Posts: 793
Concentration: Strategy, General Management
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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27 Jun 2016, 04:49
Avery's efficiency is 100/3 = 33%
tom's = 100/2.5= 40%
they worked together for 1 hour and finished 73% of the job
remaining = 27 %
tom will complete 40% in 60 minutes , 20% in 30 minutes and ,
7% in 60*7/40 minutes = 10.5 minutes
time taken by tom to finish the remaining on his own = 30+10.5 = 40.5 minutes (adjusting for the 0.333) ~ 40 minutes
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Re: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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27 Jun 2016, 08:01
1
1
Rate * Time = Work
Avery x 3 = 1
Tom y 2.5~5/2 = 1

Avery can do 1/3 work in 1 hour
Tom can do 2/5 work in 1 hour.

In 1 hour they finish 1/3+2/5 = 11/15 of work

Remaining= 1-11/15 = 4/15

Tom can do 4/15 work in
Rate*Time = Work
2/5*x=4/15
x= 4/15*5/2 =2/3 *60 = 40 minutes.

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Re: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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27 Jun 2016, 11:12
1
Bunuel wrote:
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

A. 25 minutes.
B. 30 minutes.
C. 40 minutes.
D. 55 minutes.
E. 1 hour and 20 minutes.

Avery takes 3 hours
Tom takes 2.5 hours

Let total work be 7.5 units..

Efficiency of Avery is 2.5 units/hr
Efficiency of Tom is 3 units/hr

Combined efficiency of Tom & Avery is 5.5 units/hr

Since they worked for 1 hour they completed 5.5 units of work and 2 units of work is left which is to be completed by Tom ( Since Avery left )

So Time taken by Tom to complete the remaining work will be 2/3 hours => 2/3*60 = 40 minutes...

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Re: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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29 Sep 2017, 10:33
Bunuel wrote:
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

A. 25 minutes.
B. 30 minutes.
C. 40 minutes.
D. 55 minutes.
E. 1 hour and 20 minutes.

Avery’s rate is ⅓ and Tom’s rate is 1/(2.5) = 2/5 . We can let Avery’s time = 1 hour and Tom’s time = 1 + x hours; thus:

(1/3)(1) + (1/2.5)(1 + x) = 1

1/3 + (2/5)(1 + x) = 1

Multiplying by 75, we have:

25 + 30 + 30x = 75

30 + 30x = 50

30x = 20

x = 2/3 hour = 40 minutes

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It takes Avery 3 hours to build a brick wall while Tom can do it in 2.  [#permalink]

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30 Sep 2017, 05:26
1
Bunuel wrote:
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

A. 25 minutes.
B. 30 minutes.
C. 40 minutes.
D. 55 minutes.
E. 1 hour and 20 minutes.

Despite these numbers' initial appearances, a straight combined rate approach is quick -- well under a minute.

Combined rate

Avery's rate = $$\frac{1}{3}$$

Tom's rate = $$\frac{1}{2.5} = \frac{1}{\frac{5}{2}} =\frac{2}{5}$$

$$\frac{1}{3} + \frac{2}{5} =\frac{(5+6)}{15} =\frac{11}{15}$$

Fraction of work done together

Working together at this rate for one hour, they finish $$(1)(\frac{11}{15}) = \frac{11}{15}$$ of the work

Work remaining for Tom alone

The work, 1 wall, W = $$\frac{15}{15}W$$

Fraction of work left for Tom:

$$(\frac{15}{15}W) - (\frac{11}{15}W) = \frac{4}{15}W$$ remains

Time in minutes for Tom to finish?

Time needed for Tom to finish, where $$t = \frac{W}{r}$$, and Tom's rate = $$\frac{2}{5}$$

$$\frac{\frac{4}{15}}{\frac{2}{5}}$$ = $$(\frac{4}{15}) * (\frac{5}{2}) =\frac{2}{3}hr$$

Multiply any fraction of an hour by 60 to find minutes.

$$\frac{2}{3}hr$$ * 60 = 40 minutes

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It takes Avery 3 hours to build a brick wall while Tom can do it in 2. &nbs [#permalink] 30 Sep 2017, 05:26
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