Question

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.

Answer 1

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}

Answer 2

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

v2 - v1 = 17 mph

We know, that: 
$s_1+s_2=210 \ [miles] \\ \\ t_1=t_2=2h$

So:

$v_1=\dfrac{s_1}{t_1}=\dfrac{s_1}{2} \\ \\ v_2=\dfrac{s_2}{t_2}=\dfrac{s_2}{2} \\ \\ \\ v_1+v_2= \dfrac{s_1}{2}+\dfrac{s_2}{2} \\ \\ v_1+v_2= \dfrac{s_1+s_2}{2} \\ \\ v_1+v_2= \dfrac{210}{2}=105$

NOw we've got simple system of equations:

$+\begin{cases} v_2-v_1=17 \\ v_2+v_1=105\end{cases} \\ \\ 2v_2=122 \qquad /:2 \\ \\ v_2=61 \qquad [mph] \\ \\ v_2-v_1=17 \\ \\ 61-v_1=17 \\ \\ v_1=44$

Velocities of these trains are  61mph  and 44mph