Train travel

Question

A freight train covered 120 mi at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hr shorter. how fast did the train go?

Answer 1

Let v =  the speed of the train

 

120 = vt ⇒ t = 120/v

 

120 = (v + 10)(t - 2)

 

Combine the equations above.

 

120 = (v + 10)(120/v - 2)

 

120 = 120 - 2v + 1200/v - 20

 

-2v² + 1200 - 20v = 0

 

v² + 10v - 600 = 0

 

(v - 20)(v + 30) = 0

 

v = 20 or -30

 

Choose the positive solution v = 20 miles per hour.