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The passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of passenger train, if the passenger train overtakes the freight train in three hours.

 Jan 21, 2021
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Let the rate of  the freight train  =   R

 

Let the rate of the  passenger train  be R +  30

 

The freight ttrain  has  been  traveling for 2 + 3   =  5 hours

And the passenger train has  been traveling for  3 hours

 

And they  have traveled the same distance   when  the passenger  train  overtakes the freight train

 

So    using rate * time  = distance we have that

 

R(5)  = (R + 20) 3      simplify

 

5R  =  3R  +  60     subtract 3R from  both sides

 

2R  = 60           divide  both sides  by  2

 

R = 30   (mph)  = rate of freight train

 

R +  20  =  50 (mph)    = rate of passenger train

 

cool cool cool

 Jan 21, 2021
edited by CPhill  Jan 21, 2021

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