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# Three workers, A, B, and C, can complete a certain task in 10, 5 and x

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Intern
Joined: 11 Jan 2019
Posts: 2
Three workers, A, B, and C, can complete a certain task in 10, 5 and x  [#permalink]

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12 Jan 2019, 17:28
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Hello I am new to GMAT club, and I am unsure if this is the right place to post this, but I am having trouble with what seems like a simple math problem.

Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x ?
1
1.25
2
2.5
4

I got the answer 2 through plugging in different possible answers, but I do not understand how 1/4*(1/10+1/5+1/x) gives you this answer without plugging in different possibilities.
Senior Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 365
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x  [#permalink]

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13 Jan 2019, 01:37
A (alone) completes the task in 10 hours, so in 1 hour he does 1/10 of the task
B (alone) completes the task in 5 hours, so in 1 hour he does 1/5 of the task
C (alone) completes the task in x hours, so in 1 hour he does 1/x of the task

A and B combined do : 1/10 + 1/5 = 3/10 of the task in 1 hour hour
A, B and C combined do: 1/10 + 1/5 + 1/x = 3/10 + 1/x of the task in one hour

A starts work and works for 2 hours, so he completes 1/10* 2 = 1/5 of the task
Then A & B work for next 2 hours and complete 3/10*2 = 3/5 of the task

Remaining uncompleted part = 1 - (1/5 + 3/5) = 1/5
This remaining task is done by A, B and C combined in 15 mins.
1/5 = (1/10 + 1/5 + 1/x)*15/60
so x =2
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Intern
Joined: 24 Nov 2018
Posts: 20
Location: India
Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x  [#permalink]

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13 Jan 2019, 22:33
Pick a multiple of 5 and 10 for easy calculation.
Total work can be 50
The efficiency of a = 50/10= 5
The efficiency of a = 50/5=10
The efficiency of a = 50/x

First hour: only a is working- 5 units of work
Second hour: only a is working- 5 units of work
Third hour: a: 5 units of work b: 10 units of work
Fourth hour: a: 5 units of work b: 10 units of work
Total - 40 units of work done, remaining unit- 50-40=10

10/ 5+10+(50/x)= 15/60
ie: Remaing work / efficency of all = time

25x=50
x= 2
Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x   [#permalink] 13 Jan 2019, 22:33
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