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?

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Answer 1 · 2017-10-10T18:07:03

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

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