Answer:
80 km/h
Explanation:
Let's take the origin at the bus station, x = 0.
We choose the direction of the first bus as the positive direction, so that its position at time t is
[tex]x_1(t) = v t[/tex]
where v is the speed of the bus.
The second bus travels in the opposite direction at twice the speed, 2v, so its position at time t is
[tex]x_2(t) = -2vt[/tex]
After 1 hour,
t = 1 h
The two buses are 240 km far apart, so
[tex]x_1(1)-x_2(1) = 240[/tex]
And substituting the expressions for x1 and x2, we find
[tex]vt-(-2vt)=240[/tex]
Substituting t = 1, we find v:
[tex]v -(-2v) = 240\\3v = 240\\v=\frac{240}{3}=80 km/h[/tex]
