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?
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.
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.
Answers
GPT-4o mini
Let \( r \) be the speed of the slower cyclist in miles per hour. Then, the speed of the faster cyclist would be \( 3r \) since one cyclist rides 3 times as fast as the other.
The two cyclists are riding toward each other, so their speeds can be added together to find the rate at which they are closing the distance between them.
The total distance between the two cyclists is 112 miles, and they meet after 4 hours. The equation that represents the situation is:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
Combining the speeds of both cyclists, we have:
\[
r + 3r = 4r
\]
Since they meet after 4 hours, we can write the equation as:
\[
4r \times 4 = 112
\]
Simplifying this gives:
\[
16r = 112
\]
This is the equation that can be solved to find the speed of the slower cyclist \( r \). You can now solve for \( r \), and subsequently find the speed of the faster cyclist by calculating \( 3r \).
The two cyclists are riding toward each other, so their speeds can be added together to find the rate at which they are closing the distance between them.
The total distance between the two cyclists is 112 miles, and they meet after 4 hours. The equation that represents the situation is:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
Combining the speeds of both cyclists, we have:
\[
r + 3r = 4r
\]
Since they meet after 4 hours, we can write the equation as:
\[
4r \times 4 = 112
\]
Simplifying this gives:
\[
16r = 112
\]
This is the equation that can be solved to find the speed of the slower cyclist \( r \). You can now solve for \( r \), and subsequently find the speed of the faster cyclist by calculating \( 3r \).