SOLUTION: Janet can do a job in 3 hours while Gary can do the same job in 2 hours. If Janet works for an hour before Gary helps her, how long will it take for them to finish the job together
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Question 1197196: Janet can do a job in 3 hours while Gary can do the same job in 2 hours. If Janet works for an hour before Gary helps her, how long will it take for them to finish the job together? Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Let's say the job is to move 600 boxes.
There's nothing special about the value 600. Feel free to use any other number you want, and the final answer will still be the same. I picked this value so that dividing it over 3 leads to an integer.
Janet can move 600 boxes in 3 hours if she works alone.
Her unit rate is 600/3 = 200 boxes per hour.
After 1 hour, she has moved 200 boxes.
There are 600-200 = 400 boxes left.
We're also told that Gary can do the same job in 2 hours if he works alone. His unit rate is 600/2 = 300 boxes per hour.
Combine their unit rates
200+300 = 500
Their combined unit rate is 500 boxes per hour.
This value only applies if the workers do not slow each other down.
x = number of hours they work together
(unit rate)*(time) = amount done
(500 boxes per hour)*(x hours) = 400 boxes to move
500x = 400
x = 400/500
x = 0.8 of an hour
You can put this solution on YOUR website! .
Janet can do a job in 3 hours while Gary can do the same job in 2 hours.
If Janet works for an hour before Gary helps her, how long will it take
for them to finish the job together?
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Solve it mentally, without using equations - and have fun.
Working 1 hour alone, Janet completed 1/3 of the job; hence, 2/3 of the job remained.
Janet's rate of work is 1/3 of the job per hour.
Gary's rate of work is 1/2 of the job per hour.
Their combined rate of work is = = of the job per hour.
Hence, working together, they complete the remaining 2/3 of the job in
= = = of an hour = 48 minutes.
ANSWER. Working together, they complete the remaining 2/3 of the job in 48 minutes.
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