Question

Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
b. What is the speed of the faster cyclist?
mi/hr

Answer 1

Let the speed of the slower cyclist be \( x \) miles per hour. Then, the speed of the faster cyclist is \( 3x \) miles per hour.

In 4 hours, the distance traveled by the slower cyclist is:
\[
\text{Distance} = \text{Speed} \times \text{Time} = x \times 4 = 4x \text{ miles}
\]

Similarly, the distance traveled by the faster cyclist is:
\[
\text{Distance} = 3x \times 4 = 12x \text{ miles}
\]

Since they are cycling toward each other, the total distance they cover together is equal to the distance between them:
\[
4x + 12x = 112
\]
\[
16x = 112
\]
\[
x = \frac{112}{16} = 7 \text{ miles per hour}
\]

Now, the speed of the faster cyclist is:
\[
3x = 3 \times 7 = 21 \text{ miles per hour}
\]

Thus, the speed of the faster cyclist is:
\[
\boxed{21} \text{ mi/h}
\]