SOLUTION: Nick, Kevin, and Joe can paint a room in 1 hour 20 minutes if the work together. Working alone, it takes Joe one hour more to complete the job than it takes Nick, and Nick works t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Nick, Kevin, and Joe can paint a room in 1 hour 20 minutes if the work together. Working alone, it takes Joe one hour more to complete the job than it takes Nick, and Nick works t      Log On


   

Question 863994: Nick, Kevin, and Joe can paint a room in 1 hour 20 minutes if the work together. Working alone, it takes Joe one hour more to complete the job than it takes Nick, and Nick works twice as fast as Kevin. How much time would it take each to complete the job working alone?
I convered to minutes and worked out that Nick works x minutes, Kevin 2x, and Joe x+1. Then +1%2Fx%2B1%2F%282x%29%2B1%2F%28x%2B1%29=1%2F80+, but when I solve, I don't get a real answer. I know that Nick works in 3 hours, but I don't know how to get that answer. Thanks for any help!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
All three together, 1%2F80 rooms per minute
Keeping in minutes,
Continue at Kevin, 1%2Fx rooms per minute
Nick, 1%2F%28x%2F2%29=2%2Fx
Joe, 1%2F%28x%2F2%2B60%29=1%2F%28x%2F2%2B120%2F2%29=1%2F%28%28x%2B120%29%2F2%29=2%2F%28x%2B120%29
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See that x is assigned to how many minutes Kevin can do the job by himself.
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Summarizing the list of variable and nonvariable rates for easier reading:
All three together___________1%2F80 rooms per minute
Kevin______________________1%2Fx
Nick_______________________2%2Fx
Joe______________________2%2F%28x%2B20%29