Question

Two cyclists, 30 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as

the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr

Answer 1

The speed of the slower cyclist is 2.5 mi/hr and the speed of the faster cyclist is 5 mi/hr.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the speeds of the two cyclists. Let r represent the speed of the slower cyclist. Then, the speed of the faster cyclist is 2r since they cycle 2 times as fast as the other.

We know that distance is equal to speed multiplied by time: d = r * t. For the slower cyclist, the distance traveled in 2 hours is 2r * 2 = 4r. For the faster cyclist, the distance traveled in 2 hours is 2(2r) * 2 = 8r.

Since the total distance between them is 30 miles, we can set up the equation 4r + 8r = 30 to represent this. Simplifying, we get 12r = 30.

Dividing both sides by 12, we find that r = 2.5. Therefore, the speed of the slower cyclist is 2.5 mi/hr and the speed of the faster cyclist is 2(2.5) = 5 mi/hr.