Distance, Rate, Time Problem Using Linear Equation

Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 20

mih

slower than the other. If the two buses are 512

miles apart after 4

hours, what is the rate of each bus

Answer 1

Let's let F be the speed of the faster bus and S the speed of the slower bus. Since the slower bus is 20mph slower than the faster bus, we have:

F = S + 20

And we know that after 4 hours, they're 512 miles apart and they started at the same location, so:

4(F) + 4(S) = 512.

Since we know that F = S + 20, let's use that information in the second equation.

4(F) + 4(S) = 4(S + 20) + 4(S) = 512

So 4S + 80 + 4S = 512

And 8S = 512 - 80 = 432

So S = 432 / 8 = 54 mph.

And since F = S + 20, F = 54 + 20 = 74 mph.

So the slower bus is traveling at 54 mph and the faster bus is traveling at 74 mph.