Question 1186733: One road crew can pave a section of highway in 15 h. A second crew can do the same job in 10 h. How long would it take to pave that same section of highway if both crews worked together?
Found 4 solutions by josgarithmetic, ikleyn, Alan3354, greenestamps:
Answer by josgarithmetic(39614)   (Show Source):
Answer by ikleyn(52756)  (Show Source):
You can put this solution on YOUR website! .
One road crew can pave a section of highway in 15 h.
A second crew can do the same job in 10 h.
How long would it take to pave that same section of highway if both crews worked together?
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One crew makes  of the job in each hour.
A second crew makes  of the job in each hour.
Working together, they make  =  =  =  of the job each hour.
It means that the two teams will complete the job in 6 hours, 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.
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Alan suggests in his post that there is a simple formula for such problems.
Yes, of course, it is.
But it is good to apply, when you are just familiar with the procedure and the method of solution.
I do not think that a person/(a student), just familiar with it, will come to the forum with such request -
- he (or she) will do everything on his (or her) own, without help from outside.
So, for me, if he came - he needs explanations.
After solving such problems 10 times in detailed mode, he (or she) will be able and will be ready to use the formula.
Except of it, my explanations with the rate of work make the entire class of joint work problems understandable.
Without it, the student will feel himself (or herself) as at midnight in the forest, at no moon.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! One road crew can pave a section of highway in 15 h. A second crew can do the same job in 10 h. How long would it take to pave that same section of highway if both crews worked together?
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15*10/(15+10) = 6 hours
Answer by greenestamps(13196)  (Show Source):
You can put this solution on YOUR website!
Here is another method for solving this kind of problem that is also easy to understand.
Consider the least common multiple of the two given times, which is 30 hours.
In 30 hours, the first crew could do the job 30/15=2 times; in 30 hours, the second crew could do the job 30/10=3 times.
So in 30 hours the two crews could do the job 2+3=5 times; that means together they can do the one job in 30/5=6 hours.
ANSWER: 6 hours
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