College Algebra

Question

Pat and Mike working together can assemble a bookcase in 4 minutes. It takes Mike, working by himself, 6 minutes longer than it takes Pat working by himself to assemble the bookcase. How long does it take each, working alone, to do the job?

Answer 1

Let P = Pat's time and M = Mike=s time

Remember these time are rates!

(1/P) + (1/M) = 1/4

1/M = 1/(P+6)

(1/P) + [1/P+6)] = 1/4

P² + 6P = 8P + 24

P² -2P - 24 = 0

This factors easily and gives one extraneous root and the correct answer.

You should be able to solve it from here.