SOLUTION: After 4 minutes an ant traveled 170 meters and after 7 minutes the ant will have traveled 260 meters. (a) Assuming a linear equation can be used to model the change in distance tra

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Question 889466: After 4 minutes an ant traveled 170 meters and after 7 minutes the ant will have traveled 260 meters. (a) Assuming a linear equation can be used to model the change in distance traveled over time beetween 4 and 7 minutes, write this linear model in slopeintercept form: __________ Let be the distance traveled (in meters) after minutes.(a) The ant travels at an average of 50 minutes per meter. (b) The ant travels at an average of 30 meters per minute. (c) The ant travels 50 meters in 30 minutes. (d) The ant travels at an average of 50 meters per minute. (e) The ant travels at an average of 30 minutes per meter. (c) Predict the distance that the ant will have traveled after 10 minutes and the number of minutes it will take for the ant to travel 410 meters The distance that the ant will have traveled after 10 minutes is ____________meters. (d) The number of minutes that will pass from the time the ant begins moving until it has traveled 410 meters is ____________minutes.
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After 4 minutes an ant traveled 170 meters and after 7 minutes the ant will have traveled 260 meters.
(a) Assuming a linear equation can be used to model the change in distance traveled over time between 4 and 7 minutes, write this linear model in slope intercept form: __________ Let y be the distance traveled (in meters) after x minutes.
Find the slope: %28y2-y1%29%2F%28x2-x1%29, where:
x1=4; y1=170
x2=7; y2=260
m = %28260-170%29%2F%287-4%29 = 90%2F3 = 30 is the slope
y = 30x + b
find b using x=4, y=170
30(4) + b = 170
120 + b = 170
b = 170 - 120
b = 50
therefore
y = 30x + 50 is the linear model in the slope intercept form
:
From this we can see:
(b) The ant travels at an average of 30 meters per minute.
:
(c) Predict the distance that the ant will have traveled after 10 minutes
y = 30(10) + 50
y = 350 meters in 10 min
and the number of minutes it will take for the ant to travel 410 meters
30x + 50 = 410
30x = 410-50
30x = 360
x = 360/30
x = 12 min
:
The distance that the ant will have traveled after 10 minutes is _350_ meters.
:
(d) The number of minutes that will pass from the time the ant begins moving until it has traveled 410 meters is _____12_______minutes.