SOLUTION: John can dig the garden in 30 minutes, while Jack takes 20 minutes. If they work together how many minutes would they take

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Question 1099284: John can dig the garden in 30 minutes, while Jack takes 20 minutes. If they work together how many minutes would they take
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
John makes 1%2F30 of the job per minute.

Jack makes 1%2F20 of the job per minute.

Working together they make 1%2F20+%2B+1%2F30 = 3%2F60+%2B+2%2F60 = 5%2F60 = 1%2F12 of the job per minute.


Hence, it will require 12 minutes for both to complete the job working together.

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

Tutor ikleyn's solution uses the method usually taught for solving problems like this, using the fractions of the job each worker does in a fixed unit of time.

If you are one of a large number of people who dislike fractions, here is an alternative method for solving this problem.

Consider the least common multiple of the two given times -- it is 60 minutes.
In 60 minutes, John could dig 2 of those gardens, and Jack could dig 3 of them.
So together in 60 minutes the two of them could dig 5 of them.
So the amount of time it would take them together to dig the one garden is 60/5 = 12 minutes.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Work rate can be in the unit of GARDENS per MINUTES, and then the combined rate for John and Jack working together is the sum of their rates.

JOHN, %281%2F30%29%28gardens%2Fminute%29
JACK, %281%2F20%29%28gardens%2Fminute%29

John and Jack together on the same job:
1%2F30%2B1%2F20

2%2F60%2B3%2F60

5%2F60

reduce_the_fraction

1%2F12---------------------1 garden in 12 minutes; or TWELVE MINUTES to dig ONE GARDEN