Machine $A$ working alone can complete a job in $3\frac12$ hours. Machine $B$ working alone can do the same job in

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Tue Nov 10, 2020 7:24 am

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Machine $A$ working alone can complete a job in $3\frac12$ hours. Machine $B$ working alone can do the same job in $4\frac23$ hours. How long will it take both machines working together at their respective constant rates to complete the job?

A. 1hr 10 min

B. 2hr

C. 4hr 5 min

D. 7hr

E. 8hr 10 min

Answer: B

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Tue Nov 10, 2020 7:24 am

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Re: Machine $A$ working alone can complete a job in $3\frac12$ hours. Machine $B$ working alone can do the same jo

by Scott@TargetTestPrep » Mon Nov 16, 2020 12:37 pm

Gmat_mission wrote: ↑
Tue Nov 10, 2020 7:24 am
Machine $A$ working alone can complete a job in $3\frac12$ hours. Machine $B$ working alone can do the same job in $4\frac23$ hours. How long will it take both machines working together at their respective constant rates to complete the job?

A. 1hr 10 min

B. 2hr

C. 4hr 5 min

D. 7hr

E. 8hr 10 min

Answer: B

Source: Official Guide

Solution:

We see that Machine A’s rate is 1/(7/2) = 2/7 and Machine B’s rate = 1/(14/3) = 3/14. Therefore, their combined rate is 2/7 + 3/14 = 4/14 + 3/14 = 7/14 = 1/2. Since time is the inverse of rate, the time it will take both machines working together at their respective rates to complete the job is 1/(1/2) = 2 hours.

Answer: B

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