Goran is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Goran has 68 miles to his destination after 28 minutes of driving, and he has 53.6 miles to his destination after 46 minutes of driving. How many miles will he have to his destination after 62 minutes of driving?
40.8 miles sorry for getting it wrong last time
To solve this problem, we need to find the equation of the linear function.
Let's start by defining some variables:
- Let "d" represent the distance to Goran's destination (in miles).
- Let "t" represent Goran's total driving time (in minutes).
We know that the distance to Goran's destination is a linear function of his total driving time. So we can write this function as:
d = mt + b
Where "m" is the slope of the line and "b" is the y-intercept.
Now, we can use the given information to create two equations and solve for "m" and "b".
From the first scenario, after 28 minutes, Goran has 68 miles left to his destination. So we can write the equation:
68 = m(28) + b ----(1)
From the second scenario, after 46 minutes, Goran has 53.6 miles left to his destination. So we can write the equation:
53.6 = m(46) + b ----(2)
Now, we have a system of two equations (equations 1 and 2) with two variables (m and b). We can solve this system to find the values of "m" and "b".
Subtracting equation (2) from equation (1), we get:
68 - 53.6 = m(28) - m(46) + b - b
14.4 = -18m
Dividing both sides by -18, we find:
m = -14.4 / 18
m = -0.8
Now we can substitute the value of "m" into either equation (1) or (2) to find the value of "b". Let's use equation (1):
68 = (-0.8)(28) + b
68 = -22.4 + b
Adding 22.4 to both sides of the equation, we obtain:
b = 68 + 22.4
b = 90.4
So we have determined that the equation of the linear function is:
d = -0.8t + 90.4
Now we can find the distance to Goran's destination after 62 minutes of driving by substituting t = 62 into the equation:
d = -0.8(62) + 90.4
d = -49.6 + 90.4
d = 40.8
Therefore, after 62 minutes of driving, Goran will have approximately 40.8 miles to his destination.