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

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) (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 , 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 = fraction of the job that is left

Reena must have done 1/2 the job in 1 hour before Ria joined her
Reenas rate of working is , or (1 job/2 hrs)
Let = Rias time to do the job alone

multiply both sides by

hrs
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

ok
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