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

You will have to divide

Answer 2

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

Working together the rate = 1/4
$\frac{1}{t} + \frac{1}{s} = \frac{1}{4}$

The teacher's time is 15 hrs less than the student.
$t = s -15$

Substitute into first equation, solve for "s".
$\frac{1}{s -15} + \frac{1}{s} = \frac{1}{4} \\ \\ \frac{s +(s-15)}{s(s-15)} = \frac{1}{4} \\ \\ 4s +4(s-15) = s(s-15) \\ \\ 8s -60 = s^2 -15s \\ \\ s^2 -23s+60 = 0 \\ \\ (s-20)(s-3) = 0 \\ \\ s = 20$

Therefore it would take the student 20 hours to grade.