Diana can check 25 papers in 2 hours. When Frankie helps, they can do the job together in 30 minutes. How long would it have taken Frankie to grade 25 papers b

Question

Diana can check 25 papers in 2 hours. When Frankie helps, they can do the job together in 30 minutes. How long would it have taken Frankie to grade 25 papers by himself?

Answer 1

Diana's rate per hour=1/2

x=# hours it takes Frankie alone

Frankie's rate per hour=1/x

Together it takes them 1/2 an hour (30 minutes)

(1/2)(1/2)+(1/x)(1/2)=1 (job finished)

(1/4)+(1/2x)=1

 multiply both sides by 4x

(4x)(1/4)+(4x)(1/2x)=(4x)(1)

x+2=4x

2=4x-x

2=3x

x=2/3 of an hour for Frankie alone

Check: (1/2)x+(1/[2/3])x=1 where x= time it takes them together

(1/2)x+(3/2)x=1

(4/2)x=1

2x=1

x=1/2 hour together which was stated in the problem