Same question from previous problem.
b. As the car traveled from 309 miles from Lawrence to 352 miles from Lawrence, what was the change in time in hours?
c. Define a formula that determines the distance from Lawrence in miles, d , in terms of the number of hours since passing the restaurant, t. Your formula should be in the form of an equation.
b. To find the change in time in hours, we need to subtract the initial time from the final time. Since we are given the distances traveled from Lawrence, we can use the formula for average speed to calculate the time.
Average Speed = Total Distance / Total Time
Let's assign variables for the initial and final distances:
Initial distance from Lawrence = 309 miles
Final distance from Lawrence = 352 miles
Now, let's assume the initial time is "t1" and the final time is "t2". We can set up the following equation using the average speed formula:
Average Speed = (Final Distance - Initial Distance) / (Final Time - Initial Time)
Considering the distances and time are measured from Lawrence, we can rearrange the equation as follows:
Average Speed = (352 - 309) miles / (t2 - t1) hours
We are given the average speed in the problem statement, so we can substitute that value into the equation and solve for t2 - t1:
35 mph = (352 - 309) miles / (t2 - t1) hours
To find the change in time, t2 - t1, we can rearrange the equation as follows:
(t2 - t1) hours = (352 - 309) miles / 35 mph
(t2 - t1) hours = 43 miles / 35 mph
Now we can divide 43 miles by 35 mph to get the change in time in hours.
c. To define a formula that determines the distance from Lawrence in miles, d, in terms of the number of hours since passing the restaurant, t, we can assume a constant speed. Let's denote the constant speed as "s".
Using the formula for average speed: Average Speed = Total Distance / Total Time
Considering the distance is equal to the speed multiplied by time, the equation becomes:
s = d / t
Rearranging the equation to solve for the distance, d, we get:
d = s * t
Therefore, the formula that determines the distance from Lawrence in miles, d, in terms of the number of hours since passing the restaurant, t, is:
d = s * t