Final answer:
The rate of the slower cyclist is 11 mph, while the faster cyclist's rate is 19 mph, as they were 90 miles apart after traveling in opposite directions for 3 hours.
Step-by-step explanation:
Two cyclists start at the same point and travel in opposite directions. One cyclist travels at a speed that is 8 mph faster than the other. After 3 hours, they are 90 miles apart. To find the rate of each cyclist, we start by letting the rate of the slower cyclist be x mph. Therefore, the rate of the faster cyclist is x + 8 mph.
Since they are traveling in opposite directions, their speeds are additive. After 3 hours, the total distance covered by both cyclists is the sum of the distances they individually traveled. This can be expressed as: 3 * x + 3 * (x + 8) = 90
Combining like terms and solving for x, we get:
- 3x + 3x + 24 = 90
- 6x = 66
- x = 11
Thus, the slower cyclist's rate is 11 mph, while the faster cyclist's rate is 11 mph + 8 mph = 19 mph.