SOLUTION: Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself      Log On


   



Question 293667: Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?
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Rachael rate = 1/15 job/hr.
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Together rate = 1/6 job/hr
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Jana rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/15 + 1/x = 1/6
Multiply thru by 30x to get:
2x + 30 = 5x
3x = 30
x = 10 hr (time Jana needs to do the job alone)
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Cheers,
Stan H.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
6/15+6/x=1
2/5+6/x=1
multiply by 5x
2x+30=5x
30=3x
10=x
Jana can do the job alone in 10 hrs.