SOLUTION: Shirley and Julia, working together, can finish a job in 1 hour and 20 minutes. After Shirley has worked for two hours, Julia joins her and they finish the job in 40 more minutes.

Question 184278: Shirley and Julia, working together, can finish a job in 1 hour and 20 minutes. After Shirley has worked for two hours, Julia joins her and they finish the job in 40 more minutes. How long would it have taken each woman, seperately, to do the job?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Shirley and Julia, working together, can finish a job in 1 hour and 20 minutes. After Shirley has worked for two hours, Julia joins her and they finish the job in 40 more minutes. How long would it have taken each woman, seperately, to do the job?
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Together DATA:
time = 80 min/job ; rate = 1/80 job/min
-----------------------------
Shirley DATa;
time = x min/job ; rate = 1/x job/min
In 2 hrs Shirley does 120/x job
------------------------------
Equation:
together work + Shirley work = 1 job
40(1/80) job + 120/x = 1
1/2 + 120/x = 1
Multiply thru by 2x to get:
x + 240 = 2x
x = 240 minutes (time for Shirley to do the job alone)
-------------------
Julia DATA:
time = j min/job ; rate = 1/j job/min
------------------
Equation:
Julia rate + Shirley rate = together rate
1/j + 1/240 = 1/80
Multiply thru by 240j to get:
240 + j = 3j
2j = 240
j = 120 minutes (Julia time to do the job)
==================
Cheers
Stan H.
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