distance traveled by a car you are driving at a constant spe

distance traveled by a car
you are driving at a constant speed on a freeway. at 4:30pm you drive by a signb that gives the distance to Montgomery, alabama as 84 miles AT 4:59 you drive by another sign that gives the distance to Montgomery as 56 miles.
(a) write a linear equation that gives our distance from montgomery in terms of time t(let t=0 represent 4:30pm and let t be measured in minutes

(b) use the equation in part a to find the time when you reach montgomery

so I know that it took 28 minutes to go 29 miles thats all i know

Solution

you are driving at a constant speed on a freeway. at 4:30pm you drive by a signb that gives the distance to Montgomery, alabama as 84 miles AT 4:59 you drive by another sign that gives the distance to Montgomery as 56 miles.
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(a) write a linear equation that gives our distance from montgomery in terms of time t(let t=0 represent 4:30pm and let t be measured in minutes
You have two points relating time and distance: (0,84) and (29,56)
slope = (56-84)/(29) = -28/29
Comment: That slope means the distance is reduced 28 miles in 29 minutes.
Equation Form: distance = (slope)(time in minutes) + b
Substitute and solve for \"b\":
84 = (-28/29)(0) + b
b = 84
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EQUATION:
d(t) = (-28/29)t + 84
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(b) use the equation in part a to find the time when you reach montgomery
56 = (-28/29)t + 84
(-28/29)t = - -28
(-1/29)t = -1
t = 29 minutes
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4:59 + 29 minutes = 5:28 (time of arrival at montgomery)