Question

Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker. How long does it take each to do the job alone?

Answer 1

lord I hate these types of problems

but anyway, let's let a = the number of hours it takes for the first, faster secretary to do the job alone, and b = the number of hours for the slower secretary to do the job, alone

in one hour, the a secretary does 1/a of the whole job, same logic w/ b
it says working together they do the job in 3 hours, so in one hour they do 1/3 of the whole job together

1/a + 1/b = 1/3

"Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker."

therefore b = a + 8

substituting:

1/a + 1/(a+8) = 1/3
solve for a, then you can just add 8 to get b