A motorist traveling 55 mph is being pursued by a highway patrol car traveling 65 mph. If the patrol car is four miles behind the motorist, how long will it take the patrol car to overtake the motorist?

From the moment the chase begins to the time it ends, let the time be t hrs

distance covered by motorist = 55t
distance covered by cop = 65t
65t - 55t = 4
10t = 4
t = 4/10 hours = 24 minutes

long chase.

To determine the time it will take for the patrol car to overtake the motorist, we can use a formula that relates distance, speed, and time.

Let's define the variables:
- Distance = the distance the patrol car needs to cover to catch up to the motorist (4 miles)
- Speed of the motorist = 55 mph
- Speed of the patrol car = 65 mph
- Time = the time it takes for the patrol car to overtake the motorist (what we need to find)

Now, the patrol car's speed relative to the motorist can be calculated by subtracting the motorist's speed from the patrol car's speed:
Relative Speed = Speed of the patrol car - Speed of the motorist
Relative Speed = 65 mph - 55 mph
Relative Speed = 10 mph

Since the patrol car needs to cover a distance of 4 miles to catch up to the motorist and the relative speed between them is 10 mph, we can determine the time it will take using the formula:
Time = Distance / Relative Speed
Time = 4 miles / 10 mph
Time = 0.4 hours

However, it's important to note that the time is currently in hours. To convert it to minutes, we can multiply it by 60 (since there are 60 minutes in an hour):
Time (in minutes) = Time (in hours) × 60
Time (in minutes) = 0.4 hours × 60
Time (in minutes) = 24 minutes

Therefore, it will take the patrol car approximately 24 minutes to overtake the motorist.