Question

Paul can clean a classroom floor in 3 hours. When his assistant helps him, the job takes 2 hours. How long would it take the assistant to do it alone?

Answer 1

Answer: 6 hours

Explanation:

If Paul takes 3 hours to clean the floor, then he cleans 13 of the floor per hour. His assistant takes some time t hours to do the same job, so he cleans 1t of the floor each hour. Working together, they clean the floor in 2 hours. This can be written as:

--> 1/3 + 1/t = 1/2

Multiply each side by the least common denominator, 6t.

6t(1/3+1/t)=6t(1/2)

Simplify and solve.

2t+6=3t

2t+6−2t=3t-2t

6=t