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.

Answer 1

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.