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When we talk about distance traveled, we're referring to the total length the car has covered within a certain time period. The trip odometer readings in the provided table help us measure how far the car has traveled. In this case, to find the distance traveled from 1 hour to 1.05 hours, we simply subtract the odometer reading at the beginning of the interval from the reading at the end. For instance, the odometer reading at 1 hour is 45.0 miles and at 1.05 hours it is 47.4 miles. So, the distance traveled is: \( 47.4 \text{ miles} - 45.0 \text{ miles} = 2.4 \text{ miles} \)

The time interval is the duration between two time points. In this exercise, we're looking at a time interval from 1 hour to 1.05 hours. Calculating this interval is straightforward. By subtracting the initial time from the final time, we get: \( 1.05 \text{ hours} - 1.00 \text{ hours} = 0.05 \text{ hours} \). Understanding this unit of time is crucial because it helps us determine the speed accurately. Having a specific time frame allows us to calculate how fast something is moving by knowing the distance covered within that duration.

Speed estimation involves finding out how fast the car is traveling at a particular moment. To do this, we can use the formula for average speed: \[ \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Interval}} \]. For the interval from 1 hour to 1.05 hours, we have already calculated that the distance traveled is 2.4 miles and the time interval is 0.05 hours. Plugging these values into the formula gives us: \[ \text{Average Speed} = \frac{2.4 \text{ miles}}{0.05 \text{ hours}} = 48 \text{ miles per hour} \]. To estimate the speed at exactly 1 hour into the trip, we look at a smaller time interval, such as from 0.99 hours to 1.01 hours, because shorter intervals give us a better approximation of the instantaneous speed. Using the odometer readings of 44.6 miles at 0.99 hours and 45.4 miles at 1.01 hours, we get: \( \text{Distance Traveled} = 45.4 - 44.6 = 0.8 \text{ miles} \) and \( \text{Time Interval} = 1.01 - 0.99 = 0.02 \text{ hours} \). Thus, the estimated speed is: \( \text{Estimated Speed} = \frac{0.8 \text{ miles}}{0.02 \text{ hours}} = 40 \text{ miles per hour} \). This method of speed estimation is useful for understanding how the car's speed changes over very short intervals.