Word problem help. How do I solve if I don’t know the rate or time?

Question

Suppose two trains leave Corpus Christi, Texas at the same time, traveling in opposite directions. One train travels 10 mph faster than the other. In 2.5 hours, the trains are 205 miles apart. Find the speed of each train

Answer 1

You know the travel time.  Is is given as t = 2.5 hours.

 

v = speed of one train

v + 10 = speed of the other train

 

vt + (v + 10)t = 205

 

t(2v + 10) = 205

 

t = 2.5 ⇒

 

2.5(2v + 10) = 205

 

Now you can solve for v and also get v + 10 and finish the solution.  You should get

 

v = 36 mph

v + 10 = 46 mph

 

Test the answers.