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.

Question

How many hours would it take for a student to grade all the papers on his or her own?

Answer 1

x=# of hours it takes the teacher

x+15=# of hours it takes the student

1/x=how much of the job is done in one hour by the teacher

1/(x+15)=how much of the job is done by the student in one hour

working together they take 4 hours

(1/x)(4)+(1/[x+15])(4)=1 (job done)

(4/x)+(4/[x+15])=1

multiply both sides by the LCM which is x(x+15)

(x)(x+15)(4/x)+(x)(x+15)(4/[x+15)=(x)(x+15)(1)

4(x+15)+4(x)=x^2+15x

4x+60+4x=x^2+15x

8x+60=x^2+15x

x^2+15x-8x-60=0

x^2+7x-60=0

factor

(x+12)(x-5)=0

x-5=0

x=5 hours for the teacher alone

x+15=5+15=20 hours for the student alone  (answer)