A new machine that deposits cement for a road requires 13 hours to complete a one-half mile section of road. An older machine requires 15 hours to pave the same amount of road. After depositing cement for 2 hours, the new machine develops a mechanical problem and quits working. The older machine is brought into place and continues the job. How long does it take the older machine to complete the job? (Round your answer to one decimal place.)

Question

1 h

Answer 1

d=r1*t+r2*t
job=job/13 hrs*timetotal1+job/15*timetotal2

but time total2=2 hrs
time total1 is what is to be determined

1=1/15* 2 + 1/13 * (t-2) where t is the time after the two hours left.

13*15=26+ 15t-30
15t=13*15-4
t= 12.7333 hrs check my thinking

Answer 2

The new machine completes 2/13 of the job.

So, the older machine requires (11/13)/(1/15) = 12.7 hours to do the rest.