Question

Johnny is training to run a half-marathon. His training program recommends that he run for 5 minutes and walk for 1 minute. What is the constant of proportionality and what does it mean? Also How long can Johnny run if he walks for 35 minutes?

A. The constant of proportionality is 5.
B. The constant of proportionality is 1/5.
C. The constant of proportionality is 6.
D. The constant of proportionality is 1/6.

Answer 1

The constant of proportionality in Johnny's training is 5, meaning that he runs 5 minutes for every minute he walks. Calculating how long he can run for 35 minutes of walking, Johnny can run for 175 minutes.

Step-by-step explanation:

The constant of proportionality is the fixed number that relates two variables that are directly proportional to each other. In the case of Johnny's training program, where he runs for 5 minutes and then walks for 1 minute, we can determine the constant of proportionality by the ratio of running time to walking time, which is 5/1. This gives us the constant of proportionality, which is option A: 5. This means that for every 1 minute Johnny walks, he runs for 5 minutes.

To calculate how long Johnny can run if he walks for 35 minutes, we can use the constant of proportionality and set up a proportion:

• Walk : Run = 1 : 5
• 35 : x = 1 : 5

By cross-multiplying to solve for x, we get:

• 1 * x = 5 * 35
• x = 175

Therefore, if Johnny walks for 35 minutes, he can run for 175 minutes.