SOLUTION: Russ started to mow the lawn,a task that usually takes him 40 minutes.After he had been working for 15 minutes, his friend Jay came along with his mower and began to help Russ. Wor

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Russ started to mow the lawn,a task that usually takes him 40 minutes.After he had been working for 15 minutes, his friend Jay came along with his mower and began to help Russ. Wor      Log On


   

Question 1105001: Russ started to mow the lawn,a task that usually takes him 40 minutes.After he had been working for 15 minutes, his friend Jay came along with his mower and began to help Russ. Working together, they finished the lawn in 10 minutes.How long would it taken Jay to mow the lawn by himself.
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
The Russ' rate of work is 1%2F40 of the job per  minute.

After he had been working for 15 minutes, he had done 15%2F40 = 3%2F8 of the job;  Hence, 5%2F8 of the job remained.


Then Russ and Joe completed the work in 10 minutes; hence, their combined rate of work was  %281%2F10%29%2A%285%2F8%29 = 1%2F16 of the job per minute.


It means that the Jay's individual rate of work was the difference 1%2F16 - 1%2F40 = 5%2F80 - 2%2F80 = 3%2F80 of the job per minute.


Therefore, it would take Jay 80%2F3 minutes = 26 minutes and 40 seconds to complete the job working alone.

Solved.

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It is a 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.



Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
One worker works alone for 15/40 minutes since he can do the job alone in 40 minutes
The two workers work together for 10/x minutes and 10/40 minutes
10/x+10/40+15/40=1
One worker worked 10 minutes with his partner and 15 minutes alone for a total of 25 minutes
10/x+25/40=1
10/x=1-25/40
10=(40/40-25/40)*x
10=(40-25/40)*x
10=(15/40)*x
400=15*x
400/15=x
x=26.6666667 minutes if the second worker had done the job alone
check
10/26.6666667+10/40+15/40=1
0.375+25/40=1
0.375+0.625=1
1.0=1
ok
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