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# Working together, Jeff and Ashley painted their apartment in 6 hours.

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SVP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
Posts: 1549
Location: Pakistan
GPA: 3.39
Working together, Jeff and Ashley painted their apartment in 6 hours. [#permalink]

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14 May 2017, 10:58
2
1
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:43) correct 11% (01:28) wrong based on 47 sessions

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Working together, Jeff and Ashley painted their apartment in 6 hours. If Jeff had been working alone, he could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley to paint the apartment alone?

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

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Senior Manager
Joined: 07 Jul 2012
Posts: 335
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: Working together, Jeff and Ashley painted their apartment in 6 hours. [#permalink]

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15 May 2017, 01:23
Let the no of hours taken by Ashley= A
Work done by all of them in 1 hour is given by following equation:
$$\frac{1}{10}$$+$$\frac{1}{A}$$= $$\frac{1}{6}$$

$$\frac{1}{A}$$= $$\frac{1}{6}$$-$$\frac{1}{10}$$

= $$\frac{5-3}{30}$$

$$\frac{1}{A}$$= $$\frac{2}{30}$$

A= 15 hours

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SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
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WE: Education (Education)
Re: Working together, Jeff and Ashley painted their apartment in 6 hours. [#permalink]

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15 May 2017, 02:17
Working together, Jeff and Ashley painted their apartment in 6 hours. If Jeff had been working alone, he could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley to paint the apartment alone?

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

Jeff alone = 10 Hours (6 hours + 4 hours)
Jeff and Ashley together = 6 Hours

i.e. 6 Hours work of ashley replaces 4 hours work Jeff

i.e. 6 Hours work of Ashley = 4 hours work of Jeff
i.e. 3 Hours work of Ashley = 2 hours work of Jeff

i.e. Jeff = 1.5*Ashley

i.e. (1.5A + A) take 6 hours to finish work

i.e. 2.5 A takes 6 hours to finish work
i.e. A takes 6*2.5 = 15 hours to finish the work alone

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Joined: 22 Aug 2013
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Location: India
Re: Working together, Jeff and Ashley painted their apartment in 6 hours. [#permalink]

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23 May 2017, 00:24
Take LCM of 10 & 6, which is 30
Let total work (or painting) be equivalent to 30 units

Together they take 6 hours, Jeff alone takes 10 hours. So:

Work of Jeff + Ashley together = 30/6 = 5 units per hour
Work of Jeff alone = 30/10 = 3 units per hour

Thus, work of Ashley alone = 5-3 = 2 units per hour
So, time taken by Ashley = 30/2 = 15 hours

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Re: Working together, Jeff and Ashley painted their apartment in 6 hours. [#permalink]

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25 May 2017, 15:51
Working together, Jeff and Ashley painted their apartment in 6 hours. If Jeff had been working alone, he could have painted the whole apartment in 10 hours. How many hours would it have taken Ashley to paint the apartment alone?

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

We are given that Jeff and Ashley can paint the apartment in 6 hours. If we let j = Jeff’s time to paint the apartment and a = Ashley’s time to paint the apartment, then we see that Jeff’s rate is 1/j and Ashley’s rate is 1/a. We can now create the following combined rate equation:

1/j + 1/a = 1/6

Since Jeff can paint the apartment in 10 hours, his rate is 1/10, Thus:

1/10 + 1/a = 1/6

1/a = 1/6 - 1/10

1/a = 5/30 - 3/30 = 2/30 = 1/15

Thus, Ashley can paint the apartment alone in 15 hours.

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Re: Working together, Jeff and Ashley painted their apartment in 6 hours.   [#permalink] 25 May 2017, 15:51
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