You travel 10 mi on your bicycle in the same amount
of time it takes your friend to travel 8 mi on his
bicycle. If your friend rides his bike 2 mi/h slower
than you ride your bike, find the rate at which each
of you is traveling.
Let the rate at which you travel be x mi/h. Then your friend's rate is (x-2) mi/h.
Since you both travel the same amount of time, we can set up the equation:
10/x = 8/(x-2)
Cross multiply to get:
10(x-2) = 8x
10x - 20 = 8x
2x = 20
x = 10
So, you are traveling at 10 mi/h and your friend is traveling at 8 mi/h.