SOLUTION: A train goes a distance of 120 miles at a certain speed. If the train had gone 10mph faster it would have arrived 2 hours earlier. How fast is the train going?

Question 86798This question is from textbook
: A train goes a distance of 120 miles at a certain speed. If the train had gone 10mph faster it would have arrived 2 hours earlier. How fast is the train going? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A train goes a distance of 120 miles at a certain speed. If the train had gone 10mph faster it would have arrived 2 hours earlier. How fast is the train going?
:
Let s = actual speed of the train
:
Write a time equation: Time = Distance/speed
:
Actual time = Faster speed time + 2 hrs
= + 2
:
multiply equation by s(s+10)
120(s+10) = 120s + 2(s(s+10))
120s + 1200 = 120s + 2s^2 + 20s
120s + 1200 = 2s^2 + 140s
0 = 2s^2 + 140s - 120s - 1200
2s^2 + 20s - 1200 = 0; a quadratic equation
Simplify divide by 2:
s^2 + 10s - 600 = 0
Factors to:
(s+30)(s-20) = 0
s = 20 mph
:
Check solution Using time:
120/20 = 6 hrs
120/30 = 4 hrs; 2hrs less

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