SOLUTION: Two trains made the same 150-mile run. Since one train traveled 20 mph faster than the other, it arrived 2 hours earlier. Find the speed of each train.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Two trains made the same 150-mile run. Since one train traveled 20 mph faster than the other, it arrived 2 hours earlier. Find the speed of each train.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 980070: Two trains made the same 150-mile run. Since one train traveled 20 mph faster than the other, it arrived 2 hours earlier. Find the speed of each train.
Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!

Let  u  be the speed of the faster train in mph (miles per hour).

Then the speed of the other train is  u-20 mph.
We have an equation

150%2Fu - 150%2F%28u-20%29 = 2.

Solve this equation by simplifying it step by step:

150%28u-20%29 - 150u = 2u%28u-20%29,

150u - 3000 - 150u = 2u%5E2 - 40u,

2u%5E2 - 40u - 3000 = 0,

u%5E2 - 20u - 1500 = 0.

You can solve this quadratic equation by using quadratic formula  (see the lesson  Introduction into Quadratic Equations  in this site).

Or,  you can solve it by applying the Viete's formula  (see the lesson  Solving quadratic equations without quadratic formula  in this site).

In any case,  the roots of the quadratic equation are  u%5B1%5D = 50 mph  and  u%5B2%5D = -30 mph.
Only positive value of the speed has the sense in this problem,  so that the solution is  u = 50 mph.

Answer.  The speed of the faster train is  50 mph.  The speed of the other train is  30 mph.