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Mr. Lewis made a round trip between two cities that are 200 km apart. On the return trip, he increased the average rate of travel by 5 km/h and made the trip in 2 hours less time. Find his rate of travel for each direction.

 Mar 3, 2020
 #1
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rate  * time = distance 

distance/rate = time 

     d = 200

 

x = original rate

 

200/x    =   200/(x+5) + 2      solve for x

 

200 (x+5)  =  200 x  + 2x (x+5)

200x + 1000 = 200x + 2x^2 + 10x

2x^2 +10x -1000 = 0                Use quadratic Formula    x =  20 km/hr   or  -25 (throw out)      Faster speed = 20 + 5 = 25 km/hr

 

200/20 = 10 hours          200/25 = 8 hours     Check !

 Mar 3, 2020

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