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.

gmat_guy666 wrote: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!