Question 762802: Carlisle and Springfield are 100 miles apart. If a car and a train leave Carlisle at the same, and the car travels at a rate of 25mph faster than the train, find the speed of the train if the car takes 2 hours less than the train to Springfield.
Can't even figure out where to start, should I be using a quadratic equation? Thank you so much!
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
Carlisle and Springfield are 100 miles apart. If a car and a train leave Carlisle at the same, and the car travels at a rate of 25mph faster than the train, find the speed of the train if the car takes 2 hours less than the train to Springfield.
Can't even figure out where to start, should I be using a quadratic equation? Thank you so much!
Let speed of train be S
Then speed of car = S + 25
Time train takes to travel to Springfield = 100/S
Time car takes to travel to Springfield = 100/(S + 25)
As time car takes to travel to Springfield is 2 hours less than time taken by train to travel to Springfield, we create a TIME EQUATION, which is:
Time taken by car, equals time taken by train, less 2 hours, OR
100/(S + 25) = 100/S – 2
100S = 100(S + 25) – 2(S)(S + 25) ------ Multiplying by LCD, S(S + 25)
(S - 25)(S + 50) = 0
S, or speed of train =  mph OR S = - 50 (ignore)
You can do the check!!
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