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.
If an ant walks for 10 minutes, how far will it travel in meters?
If an ant traveled 22.5 meters, how long did it walk?
What does the constant of proportionality represent in this problem?
d = k t
d in meters
t in HOURS !
so d = 18 t
=================== now it gets tricky because we need t in hours
10 minutes = 10/60 = 1/6 hours
d = 18 (1/6) = 3 meters
========================
22.5 = 18 t
t = 1.25 hours
=======================
speed in meters per hour
Meters per minute would make more sense. I do not like your problems much.
they told you that d = 18t
now what?
Thank you
You are welcome.
Thanks
To find the distance an ant will travel in a given amount of time, we can use the formula for direct variation: d = kt, where d is the distance in meters, t is the time in hours, and k is the constant of proportionality.
1. If an ant walks for 10 minutes, we first need to convert it to hours. Since there are 60 minutes in an hour, we divide 10 minutes by 60 to get 10/60 = 1/6 hours. Now we can use the formula: d = kt. Substituting the values we have, k = 18 (provided in the question), and t = 1/6, we get d = 18(1/6) = 18/6 = 3 meters. Therefore, the ant will travel 3 meters.
2. If an ant traveled 22.5 meters, we need to find the time it took. Rearranging the formula, we have t = d/k. Substituting the values we have, d = 22.5 and k = 18, we get t = 22.5/18 = 1.25 hours. Therefore, the ant walked for 1.25 hours.
3. In this problem, the constant of proportionality (k = 18) represents how many meters the ant will travel in one hour. It shows the relationship between the distance and time. As the time increases or decreases, the distance will vary proportionally according to the constant of proportionality.