On her inline skates, Haley covered a steep 10-mile route in 3 hours and 14 minutes. After a break for lunch, she took same path back to where she started from. It was mostly downhill, so she made the return trip in just 1 hour and 5 minutes later. What was her average speed during the trip?

Question

Write your answer as a whole number or as a decimal rounded to the nearest tenth.
mile

Answer 1

To find Haley's average speed for the entire trip, we first need to calculate the total distance and the total time taken.

1. Total Distance: The trip consisted of a 10-mile route going and a 10-mile return trip. Thus, the total distance is: \[ \text{Total Distance} = 10 \text{ miles} + 10 \text{ miles} = 20 \text{ miles} \]

2. Total Time:

   • The time taken for the first leg of the trip (10 miles) is 3 hours and 14 minutes. We need to convert this to hours: \[ 3 \text{ hours} + \frac{14 \text{ minutes}}{60} = 3 + \frac{14}{60} = 3 + 0.2333 \approx 3.2333 \text{ hours} \]
   • The time taken for the return trip was 1 hour and 5 minutes. Convert this time to hours as well: \[ 1 \text{ hour} + \frac{5 \text{ minutes}}{60} = 1 + \frac{5}{60} = 1 + 0.0833 \approx 1.0833 \text{ hours} \]
   • The total time for both trips is: \[ \text{Total Time} = 3.2333 \text{ hours} + 1.0833 \text{ hours} = 4.3166 \text{ hours} \]

3. Average Speed: The average speed is calculated using the formula: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{20 \text{ miles}}{4.3166 \text{ hours}} \] Performing the division: \[ \text{Average Speed} \approx 4.63 \text{ miles per hour} \]

4. Rounding to the nearest tenth: Rounding 4.63 to the nearest tenth gives: \[ \text{Average Speed} \approx 4.6 \text{ miles per hour} \]

Thus, Haley's average speed during the trip is 4.6 miles per hour.