Question

two buses leave a bus station and travel in opposite directions from that same starting point. if the speed of one is twice the speed of the other and they are 240 km apart at the end of one hour, what is the speed of each bus?​

Answer 1

80 km/h

Step-by-step 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

`x_1(t) = v t`

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

`x_2(t) = -2vt`

After 1 hour,

t = 1 h

The two buses are 240 km far apart, so

`x_1(1)-x_2(1) = 240`

And substituting the expressions for x1 and x2, we find

`vt-(-2vt)=240`

Substituting t = 1, we find v:

`v -(-2v) = 240\\3v = 240\\v=(240)/(3)=80 km/h`