adele arranges the library in 2.5 hours and her brother arranges it in 4.5 hours

Question

(a) what is the work rate of each per hour?

(b) working together, how long will it take both to arrange the library?

Answer 1

Adele arranges the library in 2.5 hours so she does

1/2.5 parts per hour or .4 parts per hour.

This can also be put in fractional terms

1/2.5 = 1/(2 1/2) = 1/(5/2) = 2/5 parts per hour

A = 2/5 parts per hour

Basically this says Adele could complete the job

2 times in 5 hours

 

Brother arranges the library in 4.5 hours so he does

1/4.5 parts per hour or = 2/9 parts per hour

B = 2/9 parts per hour

Basically this means he could complete the job

2 times in 9 hours

 

Letting x=# hours to do the work together it takes

x(A + B) = 100% or

x(2/5 + 2/9) = 1

x(18/45 + 10/45) = 1

x(28/45) = 1

x = 45/28 = 1 17/28 hours = 1.607 hours

 

Rounding to the nearest tenth it takes 1.6 hours

for Adele and her brother to arrange the library together.