What rate of time for Machine A and B ?

Question

Machine A use time more than Machine B 12 Min. for same work and If use both Machine for this work it use 8 Min.
what rate of time only Machine A.

Answer 1

Let w_a and w_b be the work rates of A and B respectively. Then we know that

w_b = 1 / 12 (i)

and

w_a + w_b = 1/8. (ii)

Substituting for w_b from (i) into (ii) yields

w_a + 1 / 12 = 1 / 8,

ie. w_a = 1 / 8 - 1 / 12 = 3 / 24 - 2 / 24 = 1 / 24.

As the work rate of A is 1 / 24, it will take 24 minutes to complete the same work as B.