Question 389456
Let S be the speed of the slow bus
Let F be the speed of the fast bus

The fast bus is 10 miles per hour faster than the slow bus. 

So, F = S + 10

Two buses depart from bus stations 360 miles apart. After two hours they are still 120 miles apart. So, after two hours they have traveled a total of 360 - 120 = 240 miles. We can express the contribution to this total by each bus by using the formula distance = speed * time, where the speeds are S and F and the time is 2 hours:

2*S + 2*F = 240
Substitute the value of F from the 1st equation:

2*S + 2*(S + 10) = 240
Distribute the 2:
2*S + 2*S + 20 = 240
4*S + 20 = 240
Subtract 20 from each side to isolate the terms with the variable:
4*S + 20 - 20 = 240 - 20
4*S = 220
Divide both sides by 4:
{{{(4*S)/4 = 220/4}}}
S = 55

And substituting 55 into the first equation
F = 55 + 10
F = 65