Jina is driving to Boston. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of โˆ’0.95

Jina has 44 miles remaining after 34 minutes of driving. How many miles will be remaining after 54 minutes of driving?

44 - 0.95 * (54-34) = 25

To find the remaining distance after 54 minutes of driving, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope (m) is -0.95. Therefore, the equation for the remaining distance is: y = -0.95x + b.

To find the y-intercept (b), we substitute the given values of x and y into the equation:

44 = -0.95(34) + b
44 = -32.3 + b

To isolate b, we add 32.3 to both sides of the equation:

b = 44 + 32.3
b = 76.3

Now we have the equation for the remaining distance:

y = -0.95x + 76.3

To find the remaining distance (y) after 54 minutes of driving (x), we substitute these values into the equation:

y = -0.95(54) + 76.3

Calculating this expression, we find:

y โ‰ˆ 24.3

Therefore, there will be approximately 24.3 miles remaining after 54 minutes of driving.

To find out how many miles will be remaining after 54 minutes of driving, we can use the information given about the linear function's slope and the remaining distance after 34 minutes.

We are told that the function gives a line with a slope of -0.95. This means that for every minute Jina drives, the remaining distance decreases by 0.95 miles.

We are also given that Jina has 44 miles remaining after 34 minutes of driving.

To find out the remaining distance after 54 minutes of driving, we can calculate the change in distance between 34 minutes and 54 minutes and subtract it from the initial remaining distance of 44 miles.

Change in Distance = Slope * Change in Time

Change in Distance = -0.95 * (54 - 34)

Change in Distance = -0.95 * 20

Change in Distance = -19

Therefore, the remaining distance after 54 minutes of driving will be:

Remaining Distance = Initial Remaining Distance - Change in Distance

Remaining Distance = 44 - (-19)

Remaining Distance = 44 + 19

Remaining Distance = 63 miles

So, after 54 minutes of driving, 63 miles will remain.