SOLUTION: Reena and Ria working together can complete a job in 1 1/2 hours. If Reena works alone for 1 hour and is then joined by Ria, the two together can finish the remaini

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Reena and Ria working together can complete a job in 1 1/2 hours. If Reena works alone for 1 hour and is then joined by Ria, the two together can finish the remaini      Log On


   

Question 132149: Reena and Ria working together can complete a job in 1 1/2 hours. If Reena works alone for 1 hour and is then joined by Ria, the two together can finish the remaining job in 3/4 hour. How long will it take each person working alone to complete the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get the rate
at which they work together
In words:
(fraction of the job)/(Reenas time) + (fraction of the job)/(Rias time) =
(fraction of the job)/(time working together)
Working together, their combined rate is 1%2F1.5, that is
(1 job/1.5 hours)
The problem says that what is left of the job after Reena works for 1 hour
can be finished by both in 3/4 hour
Let x= fraction of the job that is left
1%2F1.5+=+x%2F.75
x+=+.75%2F1.5
x+=+.5
Reena must have done 1/2 the job in 1 hour before Ria joined her
Reenas rate of working is .5%2F1+=+1%2F2, or (1 job/2 hrs)
Let r= Rias time to do the job alone
1%2F2+%2B+1%2Fr+=+1%2F1.5
1%2F2+%2B+1%2Fr+=+2%2F3
multiply both sides by 6r
3r+%2B+6+=+4r
r+=+6hrs
It will take Reena 2 hrs working alone, and
It will take Ria 6 hours working alone
check answer:
If Reena worked alone for 1 hour, she could do 1/2 of the job
so, 1/2 of the job is left
1%2F2+%2B+1%2F6+=+%281%2F2%29%2F%283%2F4%29
3%2F6+%2B+1%2F6+=+%281%2F2%29%284%2F3%29
4%2F6+=+4%2F6
ok