We know that distance = rate x time
If we say that motorcycle 1 has a speed of x, then motorcycle 2 has a speed of (x + 6)
If the two bikes start at the same point and travel in opposite directions, then we can identify the distance traveled by motorcycle 1 as d and the distance traveled by motorcycle 2 as (240 - d) since, after 6 hours, the two bikes are 240 miles apart. The time traveled is the same for both, six hours. Therefore, we have the following two equations:
d = 6x
(240 - d) = 6(x + 6)
Use the Substitution Method to solve this system of equations.
240 - 6x = 6(x + 6)
We replaced d in the second equation with 6x.
240 - 6x = 6x + 36
240 = 12x + 36
204 = 12x
x = 17
Motorcycle 1 was traveling at 17 mph, and motorcycle 2 was traveling at 17 + 6 = 23 mph
