work/rate problem..

[willbeatthegmat]

Q- Machine A & Machine B can produce 1 widget in 3hrs working together at their respective constant rates. If machine A's speed were doubled, the 2 machines cud produce 1 widget in 2 hrs working together at their respective rates. How many hrs does it currently take machine A to produce 1 widget on its own?

1/2
2
3
5
6


OA 6

[shulapa]

This question is fairly easy once you place the information given into the work/ratio formulas:
1) Rate = Work/Time
2) R1 + R2 = Rcombined

Lets assume that machine A produces a widget in a hours and that B in b hours. Therefore:
1/a + 1/b = 1/3
after the A's rate is doubled we can say that:
2/a + 1/b = 1/2

Now we can see that if we reduce the first equation from the the second, we get the vaule of a: 1/a = 1/6. Thus, a=6.