You travel 10 miles on your bicycle in the same amount of time it takes your friend to travel 8 miles 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.

3 answers

Let's call the rate at which you travel "r" (in mi/h) and the rate at which your friend travels "s" (in mi/h).

We know that you travel 10 miles in the same amount of time that your friend travels 8 miles, so we can set up the equation:

10/r = 8/s

We also know that your friend rides 2 mi/h slower than you, so we can set up another equation:

s = r - 2

Now we can substitute the second equation into the first equation:

10/r = 8/(r-2)

To solve for r, we can cross-multiply:

10(r-2) = 8r

10r - 20 = 8r

2r = 20

r = 10

So you are traveling at a rate of 10 mi/h.

To find your friend's rate, we can use the equation s = r - 2:

s = 10 - 2

s = 8

So your friend is traveling at a rate of 8 mi/h.

is that correct

Yes, that is correct!