Question

Mr. Williams is driving on a highway at an average speed of 50 miles per hour. His destination is 100 miles away. The
equation d - 100 - 50t gives the distance d (in miles) that he has left to travel as a function of the time t (in hours) that h
been driving. Write and interpret the inverse of this function (2 points per part).

Answer 1

Answer:

$d=2-\dfrac{t}{50}$.

Initial distance is 2 miles and the average speed is $\dfrac{1}{50}$ miles per hour. So, d is distance in miles that he has left to travel as a function of the time t (in hours).

Step-by-step explanation:

It is given that, mr. Williams is driving on a highway at an average speed of 50 miles per hour. His destination is 100 miles away.

The equation of distance is

$d=100-50t$     ...(1)

where, d is distance in miles that he has left to travel as a function of the time t (in hours).

We need to find the inverse of the above function.

To find the inverse, interchange variables in (1) and isolate variable d on one side.

$t=100-50d$

Subtract 100 from both sides in equation (1).

$t-100=-50d$

Divide both sides by -50.

$\dfrac{t-100}{-50}=\dfrac{-50d}{-50}$

$\dfrac{t}{-50}+2=d$

$2-\dfrac{t}{50}=d$

So, the inverse function is $d=2-\dfrac{t}{50}$.

Here, the initial distance is 2 miles and the average speed is $\dfrac{1}{50}$ miles per hour. So, d is distance in miles that he has left to travel as a function of the time t (in hours).