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?
You went (11-8) km in 15 min
that is 3/15 = 1/5 km/min
you are 8 km from home
so
8 km = (1 km/5min) * x min
x = 5 * 8 = 40 min
The minutes are the x values and how far you traveled are the y values, so it is (10,11) and (15,8). Now you have to find the slope, which is -3/5. Plug all of the numbers into y=mx+b and you get 8=-3/5(15)+b. Once you solve that, b should equal 17. Now the equation is y=-3/5x+17. Plug zero into the y value and you should get 28.33 repeated for your answer. Round that to whatever place value your problem requires, mine was to the hundredth place so my answer was 28.33.
Answer = 28.33
To solve this problem, we can use the concept of linear equations. Let's assume that the time it takes for you to reach home is denoted by 't' minutes, and the distance from home at time 't' is denoted by 'd' kilometers.
We are given two data points:
- After 10 minutes of driving, you are 11 km from home.
- After 15 minutes of driving, you are 8 km from home.
Using this information, we can set up two equations to find the unknowns:
Equation 1: 10 minutes = 11 km from home
d = mt + b
11 = m(10) + b
Equation 2: 15 minutes = 8 km from home
d = mt + b
8 = m(15) + b
We now have a system of two equations with two unknowns (m and b). By solving these equations simultaneously, we can find the values of m and b, which will allow us to determine the time it will take for you to reach home.
Subtracting Equation 2 from Equation 1:
11 - 8 = m(10) + b - m(15) - b
3 = m(10) - m(15)
3 = m(10 - 15)
3 = -5m
Dividing both sides by -5:
-3/5 = m
Substituting m = -3/5 into either equation (let's choose Equation 1):
11 = m(10) + b
11 = (-3/5)(10) + b
11 = -6 + b
b = 17
So, the equation representing the distance from home, d, in terms of time, t, is:
d = (-3/5)t + 17
Now, we want to find the time it will take for you to reach home, so we set d equal to 0 (since you'll be home when the distance is 0):
0 = (-3/5)t + 17
Solving for t:
(-3/5)t = -17
t = (-17) * (5/3)
t ≈ 28.33
Rounded to the nearest minute, you will reach home in approximately 28 minutes.