Question

A teacher can finish grading papers 15 hours before a student can. If a teacher and her student work together to grade papers, they can finish in 4 hours. How many hours would it take for a student to grade all the papers on his or her own?

Answer 1

The rate per hour = 1/time , or time = 1/rate

Working together the rate = 1/4

`(1)/(t) + (1)/(s) = (1)/(4)`

The teacher's time is 15 hrs less than the student.

`t = s -15`

Substitute into first equation, solve for "s".

`(1)/(s -15) + (1)/(s) = (1)/(4) \\ \\ (s +(s-15))/(s(s-15)) = (1)/(4) \\ \\ 4s +4(s-15) = s(s-15) \\ \\ 8s -60 = s^2 -15s \\ \\ s^2 -23s+60 = 0 \\ \\ (s-20)(s-3) = 0 \\ \\ s = 20`

Therefore it would take the student 20 hours to grade.