O Polynomial and Rational Functions
Word problem on inverse variation.

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 5 hours for a car moving at $36 \mathrm{mph}$. What is the speed of a car that makes the trip in 4 hours?

Step 1 ：Given that the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. This can be represented as \( t = \frac{k}{s} \) where \( t \) is the time, \( s \) is the speed and \( k \) is the constant of variation.

Step 2 ：We know that the trip takes 5 hours for a car moving at 36 mph. We can substitute these values into the equation to find the constant of variation \( k \). So, \( 5 = \frac{k}{36} \) which gives \( k = 5 \times 36 \).

Step 3 ：We want to find the speed of a car that makes the trip in 4 hours. We can substitute \( k \) and \( t = 4 \) into the equation to find the speed \( s \). So, \( 4 = \frac{k}{s} \) which gives \( s = \frac{k}{4} \).

Step 4 ：Substituting the value of \( k \) we found earlier, we get \( s = \frac{5 \times 36}{4} \).

Step 5 ：Calculating the above expression, we get \( s = 45 \).

Step 6 ：So, the speed of a car that makes the trip in 4 hours is \( \boxed{45} \) mph.