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.
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!
Let's denote the rate at which you are traveling as "x" mi/h. According to the given information, your friend's rate will be "x - 2" mi/h.
We can use the formula: Distance = Rate × Time.
For you: Distance = 10 miles, Rate = x mi/h, and Time is the same as your friend's.
For your friend: Distance = 8 miles, Rate = x - 2 mi/h, and Time is the same as yours.
Using the formula, we can write two equations:
10 = x × Time
8 = (x - 2) × Time
Since the time is the same in both equations, we can set them equal to each other:
10 = x × Time = 8
10 = x × Time
10 = (x - 2) × Time
Simplifying the equations, we get:
10 = x × Time
8 = x × Time - 2 × Time
Since the time is the same, we can eliminate it from the equations:
10 = x
8 = x - 2
Solving the second equation for x, we get:
8 + 2 = x
10 = x
Therefore, you are traveling at a rate of 10 mi/h, and your friend is traveling at a rate of 8 mi/h.