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

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

$y_{1} = m x$ $y_1=mx$
where $y_{1} =$ $y_1=$ distance (miles), $m =$ $m=$ speed (mph), & $x =$ $x=$ time (hours)

Thus the faster motorcyclist can be represented with this equation:

$y_{2} = (m + 2) x$ $y_2=(m+2)x$

Where $y_{2} =$ $y_2=$ the distance the faster motorcyclist travels

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

$y_{1} = m (4)$ $y_1=m(4)$
$y_{2} = (m + 2) (4)$ $y_2=(m+2)(4)$

Simplify:

$y_{1} = 4 m$ $y_1=4m$
$y_{2} = 4 m + 8$ $y_2=4m+8$

We know that $y_{1} + y_{2} = 120$ $y_1+y_2=120$ miles since we plugged in $4$ $4$ hours

So:

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

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