Train speeds?

Question

two trains going in opposite directions leace at the same time. train B travels 15mph faster than train A. In 6 hours the trains are 630 miles apart. What is the speed of both trains? 

Answer 1

Although the problem does not explicitly state this, I will assume the trains are leaving from the same station (that's the only way it makes any sense).

 

Speed is distance over time. Since the distance between them went from 0 to 630 mi in 6 hr, the speed is 105 mph. This speed can be written as v_A + v_B, since the trains are going in opposite directions. We are also told that v_B = v_A + 15. These two equations are enough to solve the problem

 

v_A + v_B = 105 --> 2v_A + 15 = 105 -->

 

v_A = 45 mph

v_B = 60 mph

Answer 2

Let x = speed of train A

 

Then, x+15 = speed of train B

 

Distance = (Rate)(Time)

 

Distance traveled by train A in 6 hours = 6x

 

Distance traveled by train B in 6 hours = 6(x+15) = 6x+90

 

In 6 hours, (Distance of train A) + (Distance of train B) = 630

 

So, 6x + 6x + 90 = 630

 

            12x + 90 = 630

 

                    12x = 540

 

                       x = 45 mph

 

The speed of train A is 45 mph and the speed of train B is 60 mph.