SOLUTION: Laura finishes a job in 5 hours but together with Bill finishes the same job in 3 hours. What percentage of the job did each person do? Since how long Bill worked to finish the s

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Laura finishes a job in 5 hours but together with Bill finishes the same job in 3 hours. What percentage of the job did each person do? Since how long Bill worked to finish the s      Log On


   

Question 1052639: Laura finishes a job in 5 hours but together with Bill finishes the same job in 3 hours. What percentage of the job did each person do?
Since how long Bill worked to finish the same job alone wasn't given, I first found out his part which was 7.5 hours or 7.53 specifically. Then I divided the total number of hours worked together by the hours each person worked so for Laura 3/5= 60% and for Bill 3/7.5= 40 percent.
I honestly have no idea if I am even close with any of the numbers such as how long Bill worked or the percentage but since I have no clue I am coming to you for help.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Constant Work-Rates Rule, R*T=J
R is rate in JOBS/TIME;
T is Time;
J is how many jobs.


Combined work rate for two agents working on the same job is the SUM of the individual rates.

Tabulating the given information can often help. 

                RATE        TIME          JOB Quantity

Laura            1/5         5             1

Bill             r                      
 
Combined        1/3          3             1

This helps to find Bill's rate.
highlight_green%281%2F5%2Br=1%2F3%29
r=1%2F3-1%2F5
r=5%2F15-3%2F15
highlight_green%28r=2%2F15%29-------Bill's rate in jobs per hour.


Now you want to calculate HOW MUCH of the job did each Bill and Laura do, when they worked together for that three hours.
-
Bill: %282%2F15%29%28jobs%2Fhours%29%2A3%28hours%29=highlight%28%282%2F5%29%2Ajob%29
Laura: %281%2F5%29%28jobs%2Fhours%29%2A3%28hours%29=highlight%28%283%2F5%29%2Ajob%29
-

You can try to check this. The sum of those two PARTS of the 1 job should be 1.
2%2F5%2B3%2F5=5%2F5=1, so this seems sensible.

You can change these to percents if you want.