Question

Two cyclists, 40 miles apart, start riding toward each other at the same time. One cycles 3 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

Let \( r \) be the speed of the slower cyclist in miles per hour. Then, the speed of the faster cyclist is \( 3r \) since he cycles 3 times as fast as the slower cyclist.

The two cyclists are riding toward each other for 2 hours, and together they will cover the distance between them, which is 40 miles.

The total distance covered by both cyclists can be expressed as:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

For 2 hours, the slower cyclist covers \( 2r \) miles, and the faster cyclist covers \( 2(3r) = 6r \) miles.

Combining the distances they travel results in:
\[
2r + 6r = 40
\]

Now combine like terms:
\[
8r = 40
\]

Now, to solve for \( r \):
\[
r = \frac{40}{8} = 5 \text{ mi/h}
\]

Now, to find the speed of the faster cyclist:
\[
\text{Speed of the faster cyclist} = 3r = 3 \times 5 = 15 \text{ mi/h}
\]

### Answers:
a. The equation is \( 8r = 40 \).

b. The speed of the faster cyclist is \( 15 \) mi/hr.