Answer:
The faster bus moves at 83mi/h and the slower one moves at 69mi/h.
Step-by-step explanation:
Let's define:
R₁ = rate of bus 1, this is the faster one.
R₂ = rate of bus 2, this is the slower one.
We know that one bus travels 14mi/h slower, then:
R₂ = R₁ - 14mi/h.
Now we know that:
Distance = Speed*Time.
If we add the distances that both busses travel in 2 hours, it should be equal to the initial distance between the buses, then:
R₁*2h + R₂*2h = 304 mi
Then we have the two equations:
R₂ = R₁ - 14mi/h
R₁*2h + R₂*2h = 304 mi
The first step is to replace the first equation in the second one, to get:
R₁*2h + (R₁ - 14mi/h)*2h = 304 mi
And now we can solve this for R₁.
R₁*2h + R₁*2h - 14mi/h*2h = 304 mi
R₁*4h - 28mi = 304mi
R₁*4h = 304mi + 28mi = 332mi
R₁ = 332mi/4h = 83mi/h
The faster bus moves at 83mi/h
And we know that the slower one moves at 14mi/h slower than this, then:
R₂ = R₁ - 14mi/h = 83mi/h - 14mi/h = 69 mi/h
