SOLUTION: peter can finish a task 8 hours, and Sam can finish the same task twice as fast as Peter. If they work together, how many hours would it take to complete the task

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Question 1194803: peter can finish a task 8 hours, and Sam can finish the same task twice as fast as Peter. If they work together, how many hours would it take to complete the task
Found 3 solutions by math_tutor2020, ikleyn, josgarithmetic:
Answer by math_tutor2020(3817) About Me  (Show Source):
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Let's say that the task is to move 80 boxes.

Peter needs 8 hours to do the task on his own.
His unit rate is 80/8 = 10 boxes per hour.

Sam works twice as fast as Peter, meaning his unit rate is 2*10 = 20 boxes per hour when Sam works alone.

If the two men work together, without hindering one another, then their combined unit rate is 10+20 = 30 boxes per hour.

x = number of hours needed to complete the task if the two men work together

(rate)*(time) = amount done
(30 boxes per hour)*(x hours) = 80 boxes total
30x = 80
x = 80/30
x = 8/3
x = (6+2)/3
x = 6/3+2/3
x = 2+2/3
x = 2 & 2/3

Answer as an improper fraction: 8/3 hours
Answer as an mixed number: 2 & 2/3 hours
Answer as a decimal: 2.67 hours approximately

Side note: 2/3 hour = (2/3)*60 = 40 minutes
Meaning that 8/3 hr = 2 & 2/3 hr = 2 hr + 40 min

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
peter can finish a task 8 hours, and Sam can finish the same task twice as fast as Peter.
If they work together, how many hours would it take to complete the task
~~~~~~~~~~~~~~ 

Peter makes 1/8 of the job per hour.  It is his rate of work.


Sam works twice as fast as Peter and makes 1/4 of the job per hour.  It is his rate of work.


Working together, they make

    1%2F8 + 1%2F4 = 1%2F8+%2B+2%2F8 = 3%2F8

of the job per hour. It is their combined rate of work.


It means that they will complete the job in 8%2F3 hours = 2 2%2F3 hours = 2 hours and 40 minutes working together.   ANSWER

Solved.

---------------

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 josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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peter can finish a task 8 hours, and Sam can finish the same task twice as fast as Peter.
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Peter, 1%2F8
Sam, 1%2F4

If they work together, then work rate is 1%2F8%2B1%2F4,.....