SOLUTION: A passenger train can travel 325 miles in the same time a freight train takes to travel 200 miles. If the speed of the passenger train is 25 mi/hr faster than the speed of the fre

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A passenger train can travel 325 miles in the same time a freight train takes to travel 200 miles. If the speed of the passenger train is 25 mi/hr faster than the speed of the fre      Log On


   

Question 65327: A passenger train can travel 325 miles in the same time a freight train takes to travel 200 miles. If the speed of the passenger train is 25 mi/hr faster than the speed of the freight train, find the speed of each. Make sure in the right hand column you give the speeds of each train.
Note: I must use algebra for this problem!
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
Freight train speed =x so the speed of the passenger train is x + 25
Time = distance/speed so
325%2F%28x%2B25%29=200%2Fx
Multiply each side by x
325x%2F%28x%2B25%29=200
Multiply each side by (x+25)
325x=200%28x%2B25%29
325x=200x%2B5000%29
Subtract 200x from each side
125x=5000%29
x=5000/125
=40 mile per hour and the passenger train speed is 65 miles per hour
(A non algebra method would take the idea that the passenger train travels an extra 125 miles and is 25 miles per hour faster so the journey would take 5 hours. The speeds would therefore be 325/5 = 65 miles per hour and 200/5=40 miles per hour)