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# One person alone can cut the grass of a yard in 4 hours. If two people

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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07 May 2017, 13:57
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Difficulty:

55% (hard)

Question Stats:

67% (02:02) correct 33% (02:20) wrong based on 182 sessions

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One person alone can cut the grass of a yard in 4 hours. If two people both working at that rate were to work on cutting the grass, but one person is to start and the other is to join him later, how long after the first person starts working should the second one join so that the task is completed in 3 hours?

A. Both should start at the same time
B. 45 minutes later
C. 1 hour later
D. 1 hour 20 minutes later
E. 2 hours later

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Re: One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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07 May 2017, 14:08
Rate per person will be 1/4 , so work done in first hour by one person =1/4 , in 2nd hour =1/4 +1/4=1/2, now after 2 hours 2nd person joins so cumulative work done in 3rd hour =1/2+1/4+1/4=1

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Director
Joined: 21 Mar 2016
Posts: 520
Re: One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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08 May 2017, 00:18
rate = 1/4
lets make use of the options,,
option A: if both start together , 1/4 + 1/4 = 1/2
time taken = 2 hrs..

option E = in 2 hrs, working alone half of the job will be completed..
remaining half can be completed if both do it in one hour
ans E
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Joined: 13 Mar 2013
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Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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15 Jul 2017, 06:50
hi ,

can anyone provide a solution using variable approach
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One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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15 Jul 2017, 11:11
Bunuel wrote:
One person alone can cut the grass of a yard in 4 hours. If two people both working at that rate were to work on cutting the grass, but one person is to start and the other is to join him later, how long after the first person starts working should the second one join so that the task is completed in 3 hours?

A. Both should start at the same time
B. 45 minutes later
C. 1 hour later
D. 1 hour 20 minutes later
E. 2 hours later

let t=1st person's time working alone
t*1/4+(3-t)*1/2=1
t=2 hours
2nd person joins 2 hours after 1st person starts
E
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Joined: 19 Jun 2017
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Re: One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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16 Jul 2017, 03:36
Suppose the second person joins after x hours.
So first person works for 3 hours and second person works for 3-x hours
together they will:
3/4 + (3-x)/4 = 1 {rate for both is same}
x = 2
Therefore, the second person joins after two hours
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Re: One person alone can cut the grass of a yard in 4 hours. If two people  [#permalink]

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16 Jul 2017, 05:53
1
abhisheknandy08 wrote:
hi ,

can anyone provide a solution using variable approach

Time taken * Efficiency = Work done.

Efficiency of $$A = B = 25%.$$

$$25t + 50(3-t) = 100$$

$$25t + 150 - 50t = 100$$

$$25t = 50$$

$$t = 2$$. Ans - E.
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Re: One person alone can cut the grass of a yard in 4 hours. If two people   [#permalink] 16 Jul 2017, 05:53
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