what is the speed of each of the two trains?

Question

a train leaves new orleans at 2:00pm. a second train leaves the same city in the same direction at 7:00pm. the second train travels 70mph faster than the first. fi the second train overtakes the first at 10:00pm, what is the speed of each of the two trains?

Answer 1

Let's let x = the speed of the first train.

 

So x + 70 is the speed of the second train.

 

Since they met at 10 PM that means that the distance traveled by each train would be the same as of that time.

 

The first train traveled for 8 hours from 2 PM to 10 PM.  And the second train traveled for 3 hours from 7 PM to 10 PM.  In other words, it takes 3 hours for the second train to travel as far as the first train travels in 8 hours.

 

The distance traveled equals the speed times the time. 

 

So the distance traveled by the first train in the 8 hours it was moving would be 8x.

 

And the distance traveled by the second train in the 3 hours it was moving would be 3 (x + 70)

 

So putting those two distances equal to each other, you get:

 

8x = 3 (x + 70)

8x = 3x + 210

5x = 210

x = 42

 

So the first train travels 42 miles per hour, and the second train travels 70 mph faster, or 112 miles per hour.