The rate per hour = 1/time , or time = 1/rate
Working together the rate = 1/4
[tex]\frac{1}{t} + \frac{1}{s} = \frac{1}{4} [/tex]
The teacher's time is 15 hrs less than the student.
[tex]t = s -15[/tex]
Substitute into first equation, solve for "s".
[tex]\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[/tex]
Therefore it would take the student 20 hours to grade.
