SOLUTION: Crane A can unload the dumpster in 10 hours, and Crane B CAN UNLOAD it in 14 hours. Crane A and B started to unload the dumpster at noon. At what time was the unloading job of the

Question 428538: Crane A can unload the dumpster in 10 hours, and Crane B CAN UNLOAD it in 14 hours. Crane A and B started to unload the dumpster at noon. At what time was the unloading job of the dumpster completed?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes to unload the dumpster with both cranes working
So, together, the two cranes unload at the rate of 1/x of the dumpster per hour
Then 12:00 noon + x=time the unloading job is completed
Crane A unloads at the rate of 1/10 of the dumpster per hour
Crane B unloads at the rate of 1/14 of the dumpster per hour
Together, they unload at the rate of 1/10 + 1/14=7/70+5/70=12/70=6/35 of the dumpster per hour
So our equation to solve is:
(6/35)*x=1 (1 dumpster, that is)
6x=35
x=5 5/6 hr=5hr 50 min ---time it takes both cranes to unload the dumpster
So 12:00 noon +5 hr 50 min=5:50 pm---time that the unloading job was completed
Another approach would be:
1/10 +1/14=1/x
6/35=1/x
6x=35
same as before

Hope this helps---ptaylor

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