Answer:
54 minutes
Step-by-step explanation:
-Let x be the work to be done.
#John's work rate per hour is:
[tex]R_j=\frac{x}{2}[/tex]
#Brenda's work rate per hour:
[tex]R_b=\frac{x}{3}[/tex]
-The amount of work done by John done after 30 minutes:
[tex]Work done=\frac{x}{2}\times \frac{1}{2}\\\\=\frac{x}{4}[/tex]
#The time it takes the two to complete the work is obtained by dividing the remaining work by their combined rate:
[tex]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[/tex]
Hence, it takes them 54 minutes to finish the job.
