A truck traveling at an average rate of 45 miles per hour leaves a rest stop. Fifteen minutes later a car traveling at an average rate of 60 miles per hour leaves the same rest stop traveling the same route. How long will it take for the car to catch up with the truck?

miles truck drove before car left rest stop = 45 * 1/4

miles an hour at which the car is catching up : 60-45 = 15 mph

how long to drive 45/4 miles at 15 mph?

To answer this question, we need to find the time it takes for the car to catch up with the truck.

Let's first convert the 15 minutes into hours. We know that there are 60 minutes in an hour, so 15 minutes is equivalent to 15/60 = 0.25 hours.

Now, let's calculate the head start of the truck. The head start is given by the formula: distance = rate × time.

The truck is traveling at an average rate of 45 miles per hour. The time it takes for the truck to travel 0.25 hours is 45 × 0.25 = 11.25 miles.

Since the car is traveling at a faster rate of 60 miles per hour, it will catch up to the truck at a rate difference of 60 - 45 = 15 miles per hour.

To find the time it takes for the car to catch up, we can divide the distance between the truck and the car (11.25 miles) by the rate difference of 15 miles per hour. This gives us: time = distance / rate = 11.25 / 15 = 0.75 hours.

Thus, it will take the car 0.75 hours, which is equivalent to 0.75 × 60 = 45 minutes, to catch up with the truck.