After the football game, the traffic out of the school parking lot is horrible! In fact, since the school is set off from town, the slow moving line of cars snakes back into town, bumper to bumper. The distance your car is from home is a linear function. When you have been crawling along for 10 minutes, you are 11 km from home, and when you have been driving for 15 minutes, you are 8 km from home. When (in minutes) will you reach home?

Question

After the football game, the traffic out of the school parking lot is horrible! In fact, since the school is set off from town, the slow moving line of cars snakes back into town, bumper to bumper. The distance your car is from home is a linear function. When you have been crawling along for 10 minutes, you are 11 km from home, and when you have been driving for 15 minutes, you are 8 km from home. When (in minutes) will you reach home?

Answer 1

you have 2 points (10, 11) and (15,8) of the form (time, distance) or (t,d)

slope = (8-11)/(15-10) = -3/5

d - 11 = (-3/5)(t - 10)

so when you are home, d = 0
0-11 = (-3/5)t + 6
(3/5)t = 17
t = .....

Answer 2

Stated somewhat more simply: It took you 5 minutes to go 3 kilometers. How many kilometers do you have left to go? Divide that by 3 and multiply that by 5.

Or, as Richard Bach wrote in "Illusions, the Adventures of a Reluctant Messiah,"
>Everything in this book may be wrong.<

Answer 3

To solve this problem, we need to find the equation of the linear function that represents the distance from home as a function of time.

Step 1: Find the slope of the line.
The slope (m) of a linear function is calculated using the formula:
m = (change in y) / (change in x)

Given that the distance decreases by 3 km in a span of 5 minutes, the change in y is -3 km and the change in x is 5 minutes. Therefore, the slope is:
m = (-3 km) / (5 minutes) = -0.6 km/minute

Step 2: Determine the y-intercept of the line.
The y-intercept (b) of a linear function is the value of y when x is zero.
To find the y-intercept, we can substitute one of the given points into the equation of the linear function.

Using the point (10, 11) where 10 minutes have passed and the distance from home is 11 km:
y = mx + b
11 = (-0.6)(10) + b
11 = -6 + b
b = 17 km

Step 3: Write the equation of the linear function.
Using the slope (m) and y-intercept (b) determined in steps 1 and 2, the equation of the linear function is:
y = -0.6x + 17

Step 4: Find when you will reach home.
To find the time (x) it takes to reach home, we substitute the distance from home (y = 0) into the equation and solve for x.

0 = -0.6x + 17
0.6x = 17
x = 17 / 0.6
x ≈ 28.33 minutes

Therefore, you will reach home in approximately 28.33 minutes.