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 x be the rate at which you are traveling in miles per hour. Then your friend is traveling at x - 2 miles per hour.
We know that time = distance / rate. Therefore, the time it takes you to travel 10 miles is 10 / x hours, and the time it takes your friend to travel 8 miles is 8 / (x - 2) hours.
Since both times are the same, we can set up the equation:
10 / x = 8 / (x - 2)
Cross multiplying, we get:
10(x - 2) = 8x
Expanding the left side:
10x - 20 = 8x
Subtract 8x from both sides:
2x - 20 = 0
Add 20 to both sides:
2x = 20
Divide by 2:
x = 10
Therefore, you are traveling at 10 miles per hour, and your friend is traveling at 8 miles per hour.