SOLUTION: Wilma can mow the lawn in 3 hours. If Kyle helps her with another mower, the lawn can be mowed in 2 hours. How long would it take Kyle if he worked alone?

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Question 1191917: Wilma can mow the lawn in 3 hours. If Kyle helps her with another mower, the lawn can be mowed in 2 hours. How long would it take Kyle if he worked alone?
Found 4 solutions by math_tutor2020, ikleyn, josgarithmetic, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let's say the lawn is 120 square feet.

Wilma can mow the lawn in 3 hours when working alone.
Her unit rate is 120/3 = 40 sq ft per hour.
In other words, she can mow 40 square feet in one hour.

If Kyle helps her, and the two don't hinder each other, then their combined unit rate is 120/2 = 60 sq ft per hour since they can get the job done in 2 hours.

This must mean Kyle's unit rate when he works alone is 60-40 = 20 sq ft per hour.
Put another way: The two workers, when doing the task alone, must have their sole unit rates add to the combined unit rate.

Since Kyle works alone to mow the grass at a rate of 20 sq ft per hour, and must mow 120 sq ft, then he'll need 120/20 = 6 hours to do the job when working alone.

An alternative approach is to solve the equation
1/3 + 1/x = 1/2
and you should find the solution is x = 6


Answer: 6 hours
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
Wilma can mow the lawn in 3 hours. If Kyle helps her with another mower,
the lawn can be mowed in 2 hours. How long would it take Kyle if he worked alone?
~~~~~~~~~~~~~~ 

Working together, they make    of the job per hour.


Wilma makes    of the job per hour.


It means that Kyle alone makes   =  =   of the job per hour.


Hence, Kyle will complete the entire job in   = 6 hours working alone.    ANSWER

Solved.

-------------------

On the way, from my exposition, you learned the conception of the rate of work.

You also learned that if you know the combined rate of work of two persons and individual rate of work
of one of them, then the rate of work of other person is the combined rate minus the known individual rate.

By knowing it, you can easily solve this and many other similar problems.


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.



Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
           SPEED          TIME,hours      LAWNS

Wilma       1/3               3             1

Kyle        1/x               x             1

Combined    1/3+1/x           2             1


-
simplest common denominator is 6x.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


A quick solution using logical reasoning instead of formal algebra....

Wilma can mow the lawn alone in 3 hours; when she and Kyle work together, it takes 2 hours.

Since 2 hours is 2/3 of 3 hours, Wilma does 2/3 of the job in those 2 hours.

That means Kyle does 1/3 of the job in those 2 hours.

And that means it would take him 6 hours to do the whole job alone.
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