Question

Two buses leave town 1404 kilometers apart at the same time and travel toward each other. one bus travels 12 km/h faster than the other. if they meet in 6 hours, what is the rate of each bus?rate of faster bus: km/hrate of slower bus: km/h

Answer 1

Let rate of faster bus be x km/h and rate of slower bus be y km /hr.

The relation between rate of slower and faster bus is,

`x=y+12`

Two bus are travelling in opposite direction so relative speed is,

`x+y`

Two buses meet in 6 hours so,

`\begin{gathered} (x+y)\cdot6=1404 \\ x+y=234 \end{gathered}`

Substitute y + 12 for x in the equation to obtain the value of y.

`\begin{gathered} y+12+y=234 \\ 2y=234-12 \\ y=(222)/(2) \\ =111 \end{gathered}`

Determine the value of x.

`\begin{gathered} x=111+12 \\ =123 \end{gathered}`

So answer is,

Rate of faster bus is 123 km/hr

Rate of slower bus is 111 km/hr.