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

Answer:

54 minutes

Step-by-step explanation:

-Let x be the work to be done.

#John's work rate per hour is:

$R_j=\frac{x}{2}$

#Brenda's work rate per hour:

$R_b=\frac{x}{3}$

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

$Work done=\frac{x}{2}\times \frac{1}{2}\\\\=\frac{x}{4}$

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

$Work \ remain=x-\frac{x}{4}=0.75x\\\\Combined \ Rate=\frac{x}{2}+\frac{x}{3}=\frac{5}{6}x\\\\time=\frac{3}{4}x\div \frac{5}{6}x\\\\=\frac{3}{4}\times \frac{6}{5}\\\\=\frac{9}{10}\times 60 \ minutes\\\\=54 \ minutes$

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