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

1 Answer
Oct 10, 2017

One motorcyclist is going 1414 mph and the other is going 1616 mph

Explanation:

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

y_1=mxy1=mx
where y_1=y1=distance (miles), m=m=speed (mph), & x=x=time (hours)

Thus the faster motorcyclist can be represented with this equation:

y_2=(m+2)xy2=(m+2)x

Where y_2=y2=the distance the faster motorcyclist travels

Plug in 44 for xx in both equations:

y_1=m(4)y1=m(4)
y_2=(m+2)(4)y2=(m+2)(4)

Simplify:

y_1=4my1=4m
y_2=4m+8y2=4m+8

We know that y_1+y_2=120y1+y2=120 miles since we plugged in 44 hours

So:

4m+4m+8=1204m+4m+8=120
8m+8=1208m+8=120
8m=1128m=112
m=14m=14

Which means one motorcyclist is going 1414 mph and the other is going 1616 mph