Julieta has been in the car with her family on a road trip for the past three hours. For the first hour, they went about 55 mph. Then, the speed limit changed and they started going about 70 mph. They are still going 70 mph.

Two and a half hours into the road trip, how far had Julieta’s family traveled?
Give your answer to a reasonable level of accuracy. Explain why your response
cannot be perfectly accurate.

1 answer

To calculate the distance Julieta's family has traveled after two and a half hours, we need to break it down into two parts, as they traveled at different speeds during the trip.

  1. First hour:

    • Speed: 55 mph
    • Time: 1 hour
    • Distance = Speed × Time = 55 mph × 1 hour = 55 miles
  2. Next hour and a half (the remaining time until 2.5 hours):

    • Speed: 70 mph
    • Time: 1.5 hours
    • Distance = Speed × Time = 70 mph × 1.5 hours = 105 miles

Now, we add the distances from both parts of the trip to find the total distance traveled:

\[ \text{Total Distance} = \text{Distance from 1st hour} + \text{Distance from next 1.5 hours} = 55 \text{ miles} + 105 \text{ miles} = 160 \text{ miles} \]

Thus, Julieta's family had traveled approximately 160 miles after two and a half hours.

Explanation of Accuracy

The response cannot be perfectly accurate for several reasons:

  1. Speed Variability: The speeds mentioned are likely average speeds, and actual driving conditions (traffic, stops, acceleration, deceleration) can cause fluctuations in speed.
  2. Measurement Precision: The speeds given (55 mph and 70 mph) are rounded figures. In reality, speeds could be slightly higher or lower, affecting the final distance.
  3. Time Representation: The times are whole numbers, and any fractional details about speed changes, stops, or deviations during the trip are not accounted for.
  4. Physical Factors: Factors such as road conditions, inclines, and vehicle performance could influence actual distance covered.

Considering these factors, while we can provide an estimate (160 miles), it may not perfectly reflect the exact distance traveled.