Let x be the rate of the slower bus, in miles per hour.

Then the rate of the faster bus is (x+18) mph, according to the condition.


The slower bus covered 5x miles before the buses meet each other.

The faster bus covered 5*(x+18) miles before they meet each other.


The sum of distances covered by buses is 3x + 5*(x+18).

It is equal exactly 760 miles. It gives you an equation


5x + 5(x+18) = 760.


Simplify and solve for x:

5x + 5x + 90 = 760,

10x = 760 - 90,

10x = 670  ====>  x =  = 67.


Thus you found the rate of the slower bus. It is 67 miles per hour.


Then the rate of the faster bus is 67 + 18 = 85 mph.