Two trains are 210 miles apart, and their speeds differ by 17 mph. find the speed of each train if they are traveling toward each other and will meet in 2 hours.

V1 - velocity first train
v2 - velocity second train
v2 > v1

v2 - v1 = 17 mph

We know, that: 


So:



NOw we've got simple system of equations:



Velocities of these trains are  61mph  and 44mph

Ok, so we know that 2 trains exist; train A and train B.

Let's say that train A travels at a speed n:

A=n

Let's also say that train B travels at a speed n-17:

B=n-17

Now, we both know that both trains will meet each other in 2 hours' time and that they were both once 210 miles apart, so let's form the equation:

2n + 2(n-17) = 210

And from here let's find out what speed n is...

2n + 2n - 34 = 210

4n - 34 = 210

4n = 244

n=244/4

Therefore, n=61.

This means that train A was travelling at 61 mph whilst train B was travelling at (61-17) mph which translates into 44 mph.

So there we have it:

Train A was travelling at 61 mph, which means that over a period of 2 hours it would have travelled a distance of 122 miles.

Train B was travelling at 44 mph, which means that over a period of 2 hours it would have travelled a distance of 88 miles.

{122 miles + 88 miles = 210 miles}