SOLUTION: A gardener completes maintenance in 12 hours. Another gardener takes 10 hours. How long will it take both gardeners?

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Question 1058134: A gardener completes maintenance in 12 hours. Another gardener takes 10 hours. How long will it take both gardeners?
Answer by ikleyn(52817) About Me  (Show Source):
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A gardener completes maintenance in 12 hours. Another gardener takes 10 hours. How long will it take both gardeners?
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The rate of the 1-st gardener is 1%2F12 job per hour.
It means that he does 1%2F12 of his job in hour. In each hour.

The rate of the 2-nd gardener is 1%2F10 job per hour.
It means that he does 1%2F10 of his job in hour. In each hour.

When they work together, their rates are added.
Together they do 1%2F12+%2B+1%2F10 of the entire work per hour.

1%2F12+%2B+1%2F10 = 10%2F120+%2B+12%2F120 = 22%2F120 of the job per hour.

Hence, they will complete the job in 120%2F22 = 60%2F11 hours = 5 5%2F11 hours.

The lesson to learn from this solution:

     There is no need to solve equations.
     You can solve it using simple logic.
     You also are supposed to operate freely with fractions. That's all.

     Simple logic and fractions.

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For a wide variety of similar solved joint-work problems with detailed explanations 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
in this site.

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".