Question

The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking. Assume that an ant's constant of proportionality is 18. Write an equation to represent the proportional relationship between d and t using the information given.

If an ant walks for 10 minutes, how far will it travel in meters?
If an ant traveled 225 meters, how long did it walk in hours?
What does the constant of proportionality represent in this problem?

Answer 1

The equation representing the proportional relationship between distance and time for an ant based on its constant of proportionality is d = 18t. An ant will travel 3 meters in 10 minutes, and if it traveled 225 meters, it walked for 12.5 hours. The constant of proportionality reflects the ant's speed of 18 meters per hour.

Step-by-step explanation:

The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking. Given that the constant of proportionality is 18, we can write the equation of the proportional relationship as d = 18t.

To find out how far an ant will travel in 10 minutes, we first convert the time to hours: 10 minutes is 10/60 hours or 1/6 hours. So, applying the equation d = 18t, we get d = 18 * (1/6) = 3 meters.

If an ant traveled 225 meters, we would set up the equation 225 = 18t, and solve for t to find that t = 225 / 18 = 12.5 hours.

The constant of proportionality in this context represents the fixed distance the ant travels in one hour, which is 18 meters per hour.