SOLUTION: It takes Dave 20 hours to paint a fence. When he works with Mike, they can paint the same fence in 4 hours. How long would it take Mike to paint the fence working alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Dave 20 hours to paint a fence. When he works with Mike, they can paint the same fence in 4 hours. How long would it take Mike to paint the fence working alone?      Log On


   

Question 866752: It takes Dave 20 hours to paint a fence. When he works with Mike, they can paint the same fence in 4 hours. How long would it take Mike to paint the fence working alone?
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/20 + 1/M = 1/4
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There are 100's of this type of problem already solved.
Look them up for further info.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = time it takes for Dave to do the job alone
y = time it takes for Mike to do the job alone
z = time it takes for them to get the job done when they work together. This is assuming that one person doesn't slow the other down and they work in the most efficient way as a team.


When we make those definitions above, it turns out that we can tie x,y,z together with this equation


1%2Fx+%2B+1%2Fy+=+1%2Fz


In this case,


x = 20
y = unknown (leave it as y for now)
z = 4


Plug those into the equation and solve for y


1%2Fx+%2B+1%2Fy+=+1%2Fz


1%2F20+%2B+1%2Fy+=+1%2F4


1%2Fy+=+1%2F4+-+1%2F20


1%2Fy+=+5%2F20+-+1%2F20


1%2Fy+=+%285+-+1%29%2F20


1%2Fy+=+4%2F20


1%2Fy+=+1%2F5


1%2A5+=+y%2A1


5+=+y


y+=+5


So it will take 5 hours for Mike to do the job alone.