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Understanding how to calculate average speed is crucial for solving distance and speed problems effectively. Average speed can be thought of as the total distance traveled divided by the total time taken to cover that distance. This is expressed with the formula: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \] To illustrate this concept, let's consider the problem scenario. During a total 100-mile journey, the student spent 2 hours on the road. We calculate the student's average speed by dividing the total distance of 100 miles by the total time of 2 hours: \[ \text{Average Speed} = \frac{100 \, \text{miles}}{2 \, \text{hours}} = 50 \, \text{mi/h} \] This means that, on average, the student covered 50 miles each hour during the trip. Calculating average speed this way helps simplify complex journeys into a single rate that represents the overall trip.

Distance calculation involves using known speed and time values to find out how far an object or person has traveled. The key formula used here is: \[ \text{Distance} = \text{Speed} \times \text{Time} \] In the problem we examined, the student drove for a duration of 1 hour and 30 minutes at a speed of 52 mi/h for the first part of the trip. There are two steps to solve for distance: - **Convert the time:** Convert 1 hour and 30 minutes into hours. Since 30 minutes is half an hour, this totals 1.5 hours. - **Apply the formula:** Multiply the speed by the time: \[ \text{Distance} = 52 \, \text{mi/h} \times 1.5 \, \text{h} = 78 \, \text{miles} \] The car covered a distance of 78 miles in the first segment of the journey. Knowing how to calculate distance helps in planning travel and estimating arrival times.

Time conversion is a vital skill in solving distance and speed problems. Often, problems will provide time in mixed units, such as hours and minutes, or require you to convert these into a consistent unit like hours. In the given travel problem, time needed to be converted from 1 hour and 30 minutes to 1.5 hours to seamlessly perform calculations. Here's how time conversion typically works: - **Understanding units:** 60 minutes equals 1 hour. Therefore, to convert minutes to hours, divide the number of minutes by 60. - **Application:** For instance, 30 minutes divided by 60 converts to 0.5 hours. Adding this to 1 hour gives 1.5 hours in total. Such conversions ensure accuracy in computations and make applying formulas more straightforward. Converting time into a single unit simplifies the equations and helps avoid mistakes.