Answer: Approximately 2.483 hours
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Step-by-step explanation:
Justin can do the full project by himself in 6 hours. This means his rate is 1/6 of a project per hour. In other words, in one hour, he gets 1/6 of the project done.
Jason can do the full project in 9 hours, so his rate is 1/9 of a project per hour, if he works alone.
Jacob's rate is 1/8 of a project per hour since he can get the job done in 8 hours if he works alone.
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So we have these unit rates
- Justin's rate = 1/6
- Jason's rate = 1/9
- Jacob's rate = 1/8
The units for each rate is projects per hour.
The total rate is
1/6 + 1/9 + 1/8
12/72 + 8/72 + 9/72
(12+8+9)/72
29/27
If the three brothers work together, and no person slows down another, then the rate at which they work together is 29/72 projects per hour. In short, they get 29/72 of the project done in 1 hour.
Let x be the number of hours needed to get the project done if they work together. Multiplying this time value with the rate leads to the amount of the project done. We want the result to be 1 to indicate a full project is complete.
(rate)*(time) = amount done
(rate)*(time) = 1 full project
(29/72)*(x) = 1
x = 1*(72/29)
x = 72/29
x = 2.48275862068966
x = 2.483
It'll take about 2.483 hours to get the job done if they work together. Again this assumes that they don't get in each others way to slow each other down.