SOLUTION: Unable to set up following question: a passenger train leaves a train depot 3 hours after a freight train leaves the same depot. The freight train is traveling 8mph slower than the

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Question 571733: Unable to set up following question: a passenger train leaves a train depot 3 hours after a freight train leaves the same depot. The freight train is traveling 8mph slower than the passenger train. Find the rate of the passenger train if the passenger train overtakes the freight train after 14.25 hours
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let p be the speed of the passenger train in mph.
The speed of the freight train, in mph, is p-8.
Multiplying the speed in mph times the time the train has been moving, we get the distance train has moved.
When the passenger train overtakes the freight train, it has been moving for 14.25 hours at speed p%7D.%0D%0AThe+distance+it+has+moved%2C+in+miles%2C+is%0D%0A%7B%7B%7B14.25p
Until it is overtaken, the freight train has been moving for 3%2B14.25 hours at speed 8-p.
The distance it has moved, in miles, is
%283%2B14.25%29%28p-8%29=17.25%28p-8%29=17.25p-17.25%2A8=17.25p-138.
Since both trains traveled the same distance,
14.25p=17.25p-138 --> 14.25p%2B138=17.28p-138%2B138 --> 14.25p%2B138=17.25p --> 14.25p%2B138-14.25p=17.25p-14.25p --> 138=%2817.25-14.25%29p --> 138=3p --> 138%2F3=3p%2F3 --> 46=p or highlight%28p=46%29