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

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

0.8 hr = 0.8*60 = 48 minutes is the final answer.

Answer by ikleyn(52781)   (Show Source): 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?
~~~~~~~~~~~~~~~~

            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.

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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