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two cranes can unloud a ship together in 12 hours. The faster crane takes 10 hours less than the slower crane, if each were to unload the same ship alone. How long does it take for each crane to unload this ship?

 Sep 30, 2023
 #1
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Rate of SLOWER crane =  1 ship /   (x -10 )

Rate of FASTER crane =   1 ship / x 

 

Now for one ship with both working the time = 12 hrs:

    1 ship /  ( 1/(x-10)  +   1/x)  =  12  hr       <====     solve for 'x' 

1 = 12/(x-10)  + 12 / x

x^2 - 10x = 12x + 12x-120

x^2 -34x +120 = 0      Use Quadrtaic Formula  ( or factoring) to find x =   30     or 4 (extraneous)

                                         so one crane takes  30 hours      the other  takes  20  hours alone     

 Oct 3, 2023

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