Question

Two motorcyclists start at the same point and travel in opposite directions. One travels 2 mph faster than the other. In 4 hours they are 120 miles apart. How fast is each​ traveling?

word problem

Answer 1

One motorcyclist is going `14` mph and the other is going `16` mph

Explanation:

You know that the slower motorcyclist can be represented with this equation:

`y_1=mx`
where `y_1=`distance (miles), `m=`speed (mph), & `x=`time (hours)

Thus the faster motorcyclist can be represented with this equation:

`y_2=(m+2)x`

Where `y_2=`the distance the faster motorcyclist travels

Plug in `4` for `x` in both equations:

`y_1=m(4)`
`y_2=(m+2)(4)`

Simplify:

`y_1=4m`
`y_2=4m+8`

We know that `y_1+y_2=120` miles since we plugged in `4` hours

So:

`4m+4m+8=120`
`8m+8=120`
`8m=112`
`m=14`

Which means one motorcyclist is going `14` mph and the other is going `16` mph