M31-25

Question

Machines A and B, working simultaneously at their respective constant rates, produce \(m\) units in 1 hour. If working independently, it takes machine B 3 hours less than machine A to produce \(2m\) units, how long does it take machine A to produce \(5m\) units?

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

Show Answer

Official Answer

E

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

Bunuel · Accepted Answer

Official Solution:

Machines A and B, working simultaneously at their respective constant rates, produce \(m\) units in 1 hour. If working independently, it takes machine B 3 hours less than machine A to produce \(2m\) units, how long does it take machine A to produce \(5m\) units?

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

Show Answer

Official Answer

E

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

On the PS section, always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question. 
 
If it takes machine B 3 hours less than machine A to produce  2m  units, then to produce  2m*2.5 = 5m  units, machine B will take  3*2.5 = 7.5  hours less than machine A. Thus, the time for A to produce  5m  units must be more than 7.5 hours. Only E fits.

Answer: E

shubham1985 · Answer

Nicely Explained Bunuel

i solved the problem in the below way. Please see whether my approach is correct. It the time taken by both A and B to complete m units of work was 1 hour, then for sure they together will take take 5 hours to complete 5m units of work. So, options A,B,and C are out. Now, to complete 2m units of work Machine B takes 3 hours less than Machine A. So, if Machine B takes 0 hour, then Machine A takes 3 hours to complete 2m units of work. Now, we need to find the time taken by machine A to finish 5m units of work. Machine B will take 7.5 hours(3hours*2.5 hours) less than machine A. So, if Machine B takes 0.1 hours to finish up the job(5m units), then Machine A alone will take 7.6 hours to finish producing 5m units of work. Only Option E fits in. Thanks ! Please press the Kudos button to appreciate

msk0657 · Answer

This one I solved via formula W = RT, R is rate and T is time. Took 3 mins of time...

Given m units of work is done by A and B in 1 hours..Let me take rate of work by A be X and rate of work by B be Y => m = (X + Y)1 => m = X + Y ------eq 1. Now A's work => 2m = XT => X = 2m/T ---eq 2. Now B's work => 2m = Y ( T - 3) => Y = 2m/T-3 ----eq 3. Sub eq 2 and 3 in eq 1. => m = 2m/T + 2m/T-3 => m(T-3)T = 2m(T-3) + 2mT. => m(T-3)T = m{ 2(T-3) + 2T} . => T^2 - 3T = 2T - 6 + 2T ( eliminating m) => T^2 - 7T + 6 = 0. => (T-6)(T-1) = 0. T = 6 or 1. Here 1 can't be the value because it has given that B has three hours less or else we get negative value. Hence it has to be 6. Sub in eq 2..... 2m = X*6 m = X * 3....because we need to find A's 5m work. For m units of work , X takes 3 hours. then for 5m units , X takes = 3 * 5m / m =15 hours.

davidbeckham · Answer

Bunuel , how do we solve this question if there was another option greater than 7.5?

Bunuel · Answer

Check alternative solutions here: https://gmatclub.com/forum/machines-a-a ... 98881.html Hope it helps.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

A_ · Answer

I like the solution - it’s helpful.

Varshal · Answer

I did not quite understand the solution. I feel the official solution presented is slightly more complex reasoning wise, it could be easier if equations were used instead (presented by other folks)

Bunuel · Answer

The official solution demonstrates an approach that will be helpful on the exam. It uses logic and creative thinking. Not all questions need to be solved using an algebraic approach. However, if you still want to check alternative solutions, you can find them here: https://gmatclub.com/forum/machines-a-a ... 98881.html

M31-25

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