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.