Omar is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Omar has 55 miles to his destination after 44 minutes of driving, and he has 41.5 miles to his destination after 62 minutes of driving. How many miles will he have to his destination after 74 minutes of driving?

After 74 minutes of driving, he still has 32.5 miles to his destination.

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's go to the question.

We know that the distance to his destination is a linear function of his total driving time.

We know that he has 55 miles to his destination after 44 minutes of driving. We can write this as the point (44 min, 55mi)

We know that he has 41.5 miles to his destination after 62 minutes of driving, we can write this as (62 min, 41.5mi)

Then the slope of this equation will be:

a = (41.5mi - 55mi)/(62min - 44min) = -0.75 mi/min.

Then the linear equation is something like:

y = (-0.75 mi/min)*x + b

to find the value of b we can use the fact that this line passes through the point (44 min, 55mi)

This means that when x = 44 min, we must have y = 55mi

Then:

55mi = (-0.75 mi/min)*44min + b

55mi + (0.75 mi/min)*44min = b

88mi  =  b

Then the equation is:

y = (-0.75 mi/min)*x + 88mi

Now we want to know how many miles will he have to his destination after 74 minutes of driving, then we need to replace x by 74 min.

y = (-0.75 mi/min)*74min + 88mi

y = 32.5mi

After 74 minutes of driving, he still has 32.5 miles to his destination.

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