SOLUTION: Jhon and Sam have a lawn mowing service. At one home, Jhon can mow the lawn by himself in 1 hours, but it takes Sam 1.5 hours. How many hours t will it take them to mow the same la

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Question 1176248: Jhon and Sam have a lawn mowing service. At one home, Jhon can mow the lawn by himself in 1 hours, but it takes Sam 1.5 hours. How many hours t will it take them to mow the same lawn together? Give the answer correct to one decimal place.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

John makes  1%2F60  of the job per minute.


Sam  makes  1%2F90  of the job per minute.


Their combined rate of work is  1%2F60 + 1%2F90 of the job per minute


    1%2F60 + 1%2F90 = 3%2F180+%2B+2%2F180 = 5%2F180 = 1%2F36  of the job per minute.


Hence, they will complete the job in 36 minutes working together.    ANSWER

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.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the standard algebraic solution method show by the other tutor.

Consider the least common multiple of the two given times. The LCM of 1 hour and 1.5 hours is 3 hours.

In 3 hours the number of such lawns Jhon could mow is 3/1 = 3; in 3 hours the number Sam could mow is 3/1.5 = 2.

So in 3 hours the two of them together could mow 3+2=5 lawns. And that means together they can mow the one lawn in 3/5 hours, or 36 minutes.