After 3 minutes an ant traveled 100 meters and after 8 minutes the ant will have traveled 175 meters.

Question

After 3 minutes an ant traveled 100 meters and after 8 minutes the ant will have traveled 175 meters.
(a)

Assuming a linear equation can be used to model the change in distance traveled over time beetween 3 and 8 minutes, write this linear model in slope-intercept form:

 

 

Let ybe the distance traveled (in meters) after xminutes.
(b)

The significance of the slope in the context of this situation is:



a.The ant travels at an average of 15 minutes per meter.


b.The ant travels at an average of 55 minutes per meter.


c.The ant travels at an average of 55 meters per minute.


d.The ant travels 55 meters in 15 minutes.


e.The ant travels at an average of 15 meters per minute.

 

 

(c)

Predict the distance that the ant will have traveled after 12 minutes and the number of minutes it will take for the ant to travel 265 meters

The distance that the ant will have traveled after 12 minutes is......... meters

 

The number of minutes that will pass from the time the ant begins moving until it has traveled 265 meters is minutes...........

Answer 1

Given:

 distance (y) = 100 m at time t = 3 min.

 distance (y) = 175 m at time t = 8 min

 

 

Let y = mt + b, where m is the slope and b is the y-intercept of the linear equation.

 

 m = (175 - 100) / (8 - 3) = 15

 

therefore, y = 15t + b

 

when t =

3, y = 100. substitute this into the above equation,

 

100 = 15(3) + b

 

b = 55

 

Finally,  y = 15t + 55 is the linear equation representing the ant's motion between 3 min to 8 min.

 

If the ant follow the same pattern, the distance that the ant will have traveled after 12 minutes is y = 15(12) + 55 = 235 meters

The number of minutes that will pass from the time the ant begins moving until it has traveled 265 meters is 265 = 15t + 55, therefore, t = 14 minutes