Respuesta :
Answer: 7.5 hours (or 7 hours 30 minutes)
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Explanation:
Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.
Through similar reasoning, Paul's rate is 1/6 of a job per hour.
Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.
Combining the three individual rates gives
1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)
1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)
1/5 + 1/6 + 1/x = (11x+30)/(30x)
The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.
Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x
(11x+30)/(30x) = 1/2
2(11x+30) = 30x*1 .... cross multiply
22x+60 = 30x
60 = 30x-22x
60 = 8x
8x = 60
x = 60/8
x = 7.5
It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.
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Here's another equation to solve though its fairly the same idea as above
1/5 + 1/6 + 1/x = 1/2
30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD
30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 15x-11x
30 = 4x
4x = 30
x = 30/4
x = 7.5
We get the same answer
Answer: 7 . 5 hrs
Step-by-step explanation:
It takes Jane 5 hours to finish the fence so she can get [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.
It takes Paul 6 hours to finish the fence so he can get [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.
It takes Peter x hours to finish the fence so he can get [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.
Together, it takes them 2 hours to finish the fence so they can get [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.
Jane + Paul + Peter = Together
[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]
Multiply everything by 30x to eliminate the denominator:
[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]
Simplify and solve for x:
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 4x
[tex]\dfrac{30}{4}=x[/tex]
7.5 = x
