Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 23, 2021 1:56 pm

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Abel can complete a work in 10 days, Ben in 12 days, and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Source: e-GMAT

Source: Beat The GMAT — Problem Solving | Sat Jan 23, 2021 1:56 pm

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Re: Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but A

by Scott@TargetTestPrep » Mon Feb 08, 2021 11:31 am

VJesus12 wrote: ↑
Sat Jan 23, 2021 1:56 pm
Abel can complete a work in 10 days, Ben in 12 days, and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Solution:

We see that rates of Abel, Ben and Carla are 1/10, 1/12 and 1/15, respectively. If we let x be the number of days the work lasted, we can create the equation:

1/10 * 2 + 1/12 * (x - 3) + 1/15 * x = 1

Multiplying the equation by 60, we have:

12 + 5x - 15 + 4x = 60

9x = 63

x = 7

Answer: B

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but A

by swerve » Tue Feb 09, 2021 3:35 am

VJesus12 wrote: ↑
Sat Jan 23, 2021 1:56 pm
Abel can complete a work in 10 days, Ben in 12 days, and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Source: e-GMAT

Amount of work Carla completed $+$ Amount of work Abel completed $+$ Amount of work Ben completed $=$ Total amount of work completed

$\dfrac{t}{15} + \dfrac{2}{10} + \dfrac{t-3}{12} = 1 \Longrightarrow t = 7$

Therefore, B

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