Question

John can complete a job in 2 hours and Brenda takes 3 hours. John works alone for 30 minutes and is then joined by Brenda. How long will it take them to finish the job together?

Answer 1

54 minutes

Explanation:

-Let x be the work to be done.

#John's work rate per hour is:

`R_j=(x)/(2)`

#Brenda's work rate per hour:

`R_b=(x)/(3)`

-The amount of work done by John done after 30 minutes:

`Work done=(x)/(2)* (1)/(2)\\\\=(x)/(4)`

#The time it takes the two to complete the work is obtained by dividing the remaining work by their combined rate:

`Work \ remain=x-(x)/(4)=0.75x\\\\Combined \ Rate=(x)/(2)+(x)/(3)=(5)/(6)x\\\\time=(3)/(4)x/ (5)/(6)x\\\\=(3)/(4)* (6)/(5)\\\\=(9)/(10)* 60 \ minutes\\\\=54 \ minutes`

Hence, it takes them 54 minutes to finish the job.