Question

two buses leave a station at the same time and travel in opposite directions. one bus travels 13 km/h slower than the other. if the two buses are 860 kilometers apart after 4 hours what is the rate of each bus?

Answer 1

One bus travels 13 km/h slower than the other.

Let x be the speed of the faster bus.

Then the speed of the slower bus is (x - 10)

The two buses are 860 kilometers apart after 4 hours

Distance = d = 860 km

Time = t = 4 hours

What is the rate (speed) of each bus?​

Recall that the relationship between speed, distance, and time is given by

`d=s\cdot t`

Where d is the distance, s is the speed, and t is the time.

The combined speed of the two buses becomes

s = x + x - 10 = 2x - 10

Now let us substitute all the values into the above formula

`\begin{gathered} d=s\cdot t \\ 860=(2x-10)\cdot4 \end{gathered}`

Now let us solve the equation

`\begin{gathered} 860=(2x-10)\cdot4 \\ 860=8x-40 \\ 860+40=8x \\ 900=8x \\ 8x=900 \\ x=(900)/(8) \\ x=22.5\: (km)/(h) \end{gathered}`

Therefore, the speed of the faster train is 22.5 km/h

The speed of the slower train is (22.5 - 10) = 11.5 km/h