Machines A and B, working simultaneously at their

[gmat_guy666]

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

OA [spoiler](E)[/spoiler]

[Brent@GMATPrepNow]

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

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

This question requires few calculations. In fact, we can just apply a bit of logic.

Machines A and B, working simultaneously at their respective constant rates produce m units in 1 hour.
IF the two machines worked at SAME speed (i.e., had the same output), this would mean that machine A (working alone) creates (1/2)m units in 1 hour.

...working independently it takes machine B 3 hours less than machine A to produce 2m units
This tell us that machine B is FASTER than machine A.
So, we can conclude that machine A (working alone) creates FEWER THAN (1/2)m units in 1 hour.

How long does it take machine A to produce 5m units?
IF machine A (working alone) creates (1/2)m units in 1 hour, then it would take 10 hours to produce 5m units.
Since machine A (working alone) creates FEWER THAN (1/2)m units in 1 hour, then it would take MORE THAN 10 hours to produce 5m units.

Only answer choice E meets this condition.

Cheers,
Brent

[DavidG@VeritasPrep]

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

Backsolve!

(Let's say m = 1, so 2m = 2, and 5m = 5.)

Sometimes I like to start at the bottom and work up.

Say it takes A 15 hours to produce 5 units. So A's rate is 5 units/15 hours or 1 unit/3 hours.

We know that together they can make 1 unit an an hour. So

1/3 + Rate B = 1. Rate B = 2/3. Thus B could make 2 units every 3 hours.

We also know that the time it takes B to make 2 units should be 3 hours less than the time it takes A to make 2 units. We discovered that it takes B 3 hours to make 2 units. If A makes 1 unit every 3 hours, it will take A 6 hours to make 2 units. If it takes B 3 hours to make 2 units, and it takes A 6 hours to make 2 units, we have our 3 hour difference. E is the answer.

[GMATGuruNY]

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

Let m=6 units, implying that 2m=12 units and that 5m=30 units.
We can PLUG IN THE ANSWERS, which represent A's time to produce 5m units.
When the correct answer choice is plugged in, A's time produce 12 units will be 3 hours more than B's time.

Answer choice D: 6 hours
Since A takes 6 hours to produce 30 units, A's rate = w/t = 30/6 = 5 units per hour.
Since A and B together take 1 hour to produce 6 units, A and B's combined rate = w/t = 6/1 = 6 units per hour.
Thus:
B's rate = (combined rate for A and B together) - (A's rate alone) = 6-5 = 1 unit per hour.
Time for A to produce 2m units = w/r = 12/5 = 2.4 hours.
Time for B to produce 2m units = w/r = 12/1 = 12 hours.
Here, A's time is LESS than B's time.
Since A must take 3 hours LONGER than B, A's time to produce 5m units must INCREASE.

The correct answer is E.

Answer choice E: 15 hours
Since A takes 15 hours to produce 30 units, A's rate = w/t = 30/15 = 2 units per hour.
Since A and B together take 1 hour to produce 6 units, A and B's combined rate = w/t = 6/1 = 6 units per hour.
Thus:
B's rate = (combined rate for A and B together) - (A's rate alone) = 6-2 = 4 units per hour.
Time for A to produce 2m units = w/r = 12/2 = 6 hours.
Time for B to produce 2m units = w/r = 12/4 = 3 hours.
A's time - B's time = 6-3 = 3 hours.
Success!