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

[Gmat_mission]

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

[Scott@TargetTestPrep]

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