Question

Two buses leave towns 296 miles apart at the same time and travel toward each other. One bus travel 18 mi/h slower than the other.If they meet in 2 hours, what is the rate of each bus?rate of slower bus_____rate of the faster bus___

Answer 1

Let:

x = rate of the slower bus

y = rate of the faster bus

One bus travel 18 mi/h slower than the other, so:

`x=y-18`

the buses leave towns 296 miles apart at the same time and they meet in 2 hours, so:

`\begin{gathered} 2x+2y=296 \\ where \\ x=y-18 \\ 2(y-18)+2y=296 \\ 2y-36+2y=296 \\ 4y-36=296 \\ 4y=296+36 \\ 4y=332 \\ y=(332)/(4) \\ y=(83mi)/(h) \end{gathered}`

Replace the value of y into:

`\begin{gathered} x=y-18 \\ x=83-18 \\ x=(65mi)/(h) \end{gathered}`

Answer:

rate of slower bus:

`(65mi)/(h)`

rate of the faster bus:

`(83mi)/(h)`