Two cyclists, 96 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?

Let's define the variables and set up the equations to solve the problem.

Let the speed of the slower cyclist be \( x \) miles per hour (mi/h). Since one cyclist is cycling three times as fast as the other, the speed of the faster cyclist will be \( 3x \) mi/h.

The cyclists are moving towards each other, so their combined speed is the sum of their individual speeds, i.e., \( x + 3x = 4x \) mi/h.

They meet after 4 hours, and during this time they cover a distance of 96 miles (the distance between them). Therefore, the total distance covered is:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
96 = 4x \times 4
\]

Simplifying this equation:

\[
96 = 16x
\]

Solving for \( x \):

\[
x = \frac{96}{16} = 6 \, \text{mi/h}
\]

Thus, the speed of the slower cyclist is 6 mi/h. Since the faster cyclist is 3 times as fast, the speed of the faster cyclist is:

\[
3x = 3 \times 6 = 18 \, \text{mi/h}
\]

Therefore, the speed of the faster cyclist is **18 mi/h**.

Would you like more details on any part of this solution?

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Here are 5 related questions you might find interesting:

1. If the slower cyclist's speed was 8 mi/h, how much time would it take for them to meet?
2. What would happen if the distance between the cyclists was doubled?
3. If they met after 6 hours instead of 4, what would be the speed of the faster cyclist?
4. How much distance would the slower cyclist cover before they meet?
5. What if the faster cyclist's speed was halved—how long would it take to meet?

**Tip:** When solving problems with relative motion, combining the speeds of both objects moving towards each other simplifies calculations!

Solve a relative motion problem where two cyclists, 96 miles apart, ride toward each other. One cyclist travels 3 times faster than the other. Learn how to calculate the speed of the faster cyclist using algebra and motion formulas. Suitable for students in Grades 6-8.

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