SOLUTION: Larry and Curly are trying to fill a sandbox with sand. Working alone, Larry can fill an empty sandbox in 4 hours, and Curly can do the same job in 5 hours. Moe is trying to empt

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Larry and Curly are trying to fill a sandbox with sand. Working alone, Larry can fill an empty sandbox in 4 hours, and Curly can do the same job in 5 hours. Moe is trying to empt      Log On


   

Question 948440: Larry and Curly are trying to fill a sandbox with sand. Working alone, Larry can fill an empty
sandbox in 4 hours, and Curly can do the same job in 5 hours. Moe is trying to empty the
sandbox. Working alone, Moe can empty a full sandbox in 6 hours. If the sandbox is half
full at the time Larry and Curly begin filling the sandbox and Moe begins emptying it, how
many minutes will it take for the sandbox to be filled? Express your answer to the nearest
whole number.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Larry fills one sand box in four hours or 1 box/4hrs= 1/4 box/hr
Curly fills one sand box in five hours or 1 box/5hrs= 1/5 box/hr
Moe empties one sand box in six hours or -1 box/6hrs= -1/6 box/hr
All together:(Find common denominator and add)
1+box%2F4+hr%2B1+box%2F5+hr-1+box%2F6+hr=15+box%2F60hr%2B12box%2F60hr-10box%2F60hr=17box%2F60hr
With half already full, 30/60 box remains to fill at the rate of 17/60 box/hr:
(30/60 box)/(17/60 box/hr)=1.765 hrs=105.88 minutes
ANSWER: With all three working, it will take 106 minutes to finish filling the last half of the sand box.