Work problem - MGMAT CAT 3

josh80 wrote:Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?


1/2

2

3

5

6

We can plug in the answers, which represent A's time to produce 1 widget.
Since A and B working together take 3 hours to produce 1 widget, A working alone must take MORE than 3 hours.
Eliminate A, B and C.

Let the value of each widget = 30 units.
Since A and B together take 3 hours to produce 1 widget, their combined rate = w/r = 30/3 = 10 units per hour.

Answer choice D: 5 hours for A alone
Since A alone takes 5 hours to produce 1 widget, A's rate alone = 30/5 = 6 units per hour.
Thus, B's rate alone = (combined rate for A and B) - (A's rate alone) = 10-6 = 4 units per hour.
When A's rate is doubled, the new combined rate for A and B = 2*6 + 4 = 16 units per hour.
Time to produce 1 widget when A's rate is doubled = w/r = 30/16 = 15/8 hours.
Since the required time is 2 hours, eliminate D.

The correct answer is E.

Answer choice E: 6 hours for A alone
Since A alone takes 6 hours to produce 1 widget, A's rate alone = 30/6 = 5 units per hour.
Thus, B's rate alone = (combined rate for A and B) - (A's rate alone) = 10-5 = 5 units per hour.
When A's rate is doubled, the new combined rate for A and B = 2*5 + 5 = 15 units per hour.
Time to produce 1 widget when A's rate is doubled = w/r = 30/15 = 2 hours.
Success!