During rush hour Bill can drive 15 miles using the sideroads

During rush hour, Bill can drive 15 miles using the sideroads in the same time that it takes to travel 10 miles on the freeway. If Bills rate on the side roads is 8mi/h faster than his rate on the freeway, find his rate on the side roads.

Solution

Let x=Bill\'s rate on the freeway
Then x+8=His rate on the side roads
Distance(d)=Rate(r) times Time(t) or d=rt
and t=d/r
time it takes on the freeway=10/x
time it takes on the side roads=15/(x+8)
Now we are told that these times are the same, therefore:
10/x=15/(x+8) Multiply by both sides by x(x+8) and we get:
10(x+8)=15x or
10x+80=15x subtract 10x from both sides:
80=15x-10x
5x=80
x=16 mph on the freeway
x+8=16+8=24 mph on the side roads
ck
10/16=15/24
5/8=5/8
and
16+8=24
24=24