SOLUTION: Bob can plant a garden by her self in 10 hours. When her son Andrew helps her the total time it takes them to plant the garden is 4 hours. How long would it take Andrew to plant th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Bob can plant a garden by her self in 10 hours. When her son Andrew helps her the total time it takes them to plant the garden is 4 hours. How long would it take Andrew to plant th      Log On


   

Question 1131129: Bob can plant a garden by her self in 10 hours. When her son Andrew helps her the total time it takes them to plant the garden is 4 hours. How long would it take Andrew to plant the garden himself
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Working together, Bob and Andrew make  1%2F4  of the job per hour.


Working alone, Bob makes  1%2F10  of the job per hour.


Hence, working alone, Andrew makes  1%2F4 - 1%2F10 = 5%2F20+-+2%2F20 = 3%2F20  of the job per hour.


It means that Andrew needs  20%2F3 hours = 62%2F3 hours = 6 hours and 40 minutes to complete the job working alone.    Answer

Solved.

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The lessons to learn from this solution : 

    1)  You can solve this problem/(such problems) even without using equations.

        Freely manipulating with fractions is enough.


    2)  Use the notion "rate of work" and remember:

            a)  when two persons work together, their combined rate of work is the sum of individual rates;


            b)  when the combined rate of two workers is given along with the rate of one of them, the rate 
                of the other worker is the difference of combined rate and the given individual rate.


Very simple rules, and they allow to solve  MANY  OF  SIMILAR  PROBLEMS.

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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 method for solving "working together" problems that the other two tutors have shown.

Consider the least common multiple of the two times given, 4 hours and 10 hours. The least common multiple is 20 hours.

Bob can plant a garden in 10 hours, so in 20 hours she can plant 2 of those gardens.

Together, Bob and her son Andrew can plant the garden in 4 hours, so in 20 hours together they could plant 5 of those gardens.

So in those 20 hours Bob can plant 2 of the gardens, and Bob and Andrew together can plant 5 of them; that means in 20 hours Andrew alone can plant 3 of them.

And so the time Andrew alone takes to plant the one garden is 20/3 hours, or 6 2/3 hours.