91Ó°ÊÓ

Average speed is a key concept when discussing travel time calculations, as it helps us figure out how long a trip will take. To calculate average speed, you simply need to divide the total distance traveled by the total time it takes to travel that distance.
So, the formula is:

• \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

In the case of the Sacramento to San Francisco trip, on a regular day, the average speed is 105 km/hr. This means that, on average, for every hour traveled, the car covers a distance of 105 kilometers.
This understanding of average speed allows you to predict travel times by simply knowing the distance and speed. On Fridays, due to traffic slowing us down to 70 km/hr, it means each kilometer takes slightly longer to travel.

The distance formula is handy in solving problems where you need to find out how far you will travel. It is expressed as:

• \( \text{Distance} = \text{Speed} \times \text{Time} \)

This formula helps in calculating the exact distance covered over a specific period, given the speed. For the usual trip between Sacramento and San Francisco, this was used with a speed of 105 km/hr and a time of 1.333 hours. This calculation results in a distance of 140 km.
Understanding this formula enables you to rearrange terms to solve for any variable, so you can rearrange it as needed to find time or speed if distance is known.

Time conversion is often necessary when calculating travel times because the units of time and speed must match. Here, converting minutes to hours is crucial.
Since there are 60 minutes in an hour, you can convert minutes into hours by dividing the number of minutes by 60. For example, 20 minutes is converted to 0.333 hours because:

• \( \frac{20}{60} = 0.333 \text{ hours} \)

This step is vital in ensuring the time calculations are correct. In our problem, 1.0 hour and 20 minutes became 1.333 hours, allowing for direct multiplication with speed in km/hr.

The relationship between speed, distance, and time is deeply interconnected and fundamental for solving travel time problems. When you know two of these variables, you can always find the third by rearranging the formula:

• \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
• \( \text{Distance} = \text{Speed} \times \text{Time} \)
• \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)

In our problem, we calculate how long the trip takes on a Friday when traffic reduces speed to 70 km/hr, maintaining the distance of 140 km. The time taken becomes longer due to the reduced speed:

• \( \text{Time} = \frac{140 \text{ km}}{70 \text{ km/hr}} = 2 \text{ hours} \)

Understanding these relationships helps in planning and predicting travel times effectively, accounting for various speeds due to conditions like traffic.