Question

to cyclist, 144 miles apart, started 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?
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. and what is the speed of the faster cyclist?
mi/hr

Answer 1

To solve the problem, we can use the following steps.

### a. Write an equation
Let \( r \) be the speed of the slower cyclist in miles per hour. Then, the speed of the faster cyclist, who is cycling three times as fast, would be \( 3r \) miles per hour.

Since they are cycling toward each other, their combined speed is:
\[ r + 3r = 4r \, \text{miles per hour} \]

They will meet after 4 hours, and the total distance they travel together will equal the distance apart, which is 144 miles. We can write the equation based on distance = speed × time:
\[
4r \times 4 = 144
\]

### b. Calculate the speed of the faster cyclist
Now we can solve the equation:
\[
16r = 144
\]

To find \( r \), divide both sides by 16:
\[
r = \frac{144}{16} = 9 \, \text{mi/h}
\]

Now that we have the speed of the slower cyclist, we can find the speed of the faster cyclist:
\[
\text{Speed of the faster cyclist} = 3r = 3 \times 9 = 27 \, \text{mi/h}
\]

Thus, the speed of the faster cyclist is **27 miles per hour**.