SOLUTION: Two cranes, operating together, can unload a cargo ship in 4 hours. If it takes one crane twice as long as the other to unload the ship, how long would it take each crane to unload

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Question 178779: Two cranes, operating together, can unload a cargo ship in 4 hours. If it takes one crane twice as long as the other to unload the ship, how long would it take each crane to unload the ship by itself?
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
let y and x be the time crane 1 and crane 2, respectively, take to unload the ship by themselves. y=2x
:
crane 1 does 1/2x of the job per hour
:
crane 2 does 1/x of the job per hour
:
(1/x+1/2x)(4)=1job
:
((2+1)/2x)4=1
:
12/2x=1
:
2x=12=
:
hours-time for crane 2 to do the job
:
y=2xhours-time for crane 1 to do the job

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let x be the number of hours it takes thing A to do one job. Then thing A can do of the job in 1 hour. If thing B takes twice as long, then 2x represents the number of hours it takes thing B to do the same job, and thing B can do of the job in 1 hour.

Together, thing A and thing B can do of the job in 1 hour.

That means that thing A and thing B can do the entire job in hours.

But we are given that thing A and B can do the entire job in 4 hours.

Solve for x in to get the time it takes A to do the job, and double it to get the time for thing B.

Notice I described this as 'thing A' and 'thing B' and just called what they were doing a 'job' That's because this method works for 'painting a room' questions, 'two different sized pipes filling or emptying a tank' problems, and anything else like it.