Pooja hiked at a speed of 3 mph for 5 hours and then took a 2-hour break. After the break, Pooja's mother picked her up in a car and they drove home in 30 minutes at a speed of 60 mph. What was the average speed of Pooja's entire trip, including her break?

Answer 1

To find the average speed of Pooja's entire trip, we first need to determine the total distance she traveled and the total time spent for the trip, including the break.

1. Distance Pooja Hiked:

   • Speed = 3 mph
   • Time = 5 hours
   • Distance = Speed × Time = \( 3 , \text{mph} \times 5 , \text{hours} = 15 , \text{miles} \)

2. Time Taken:

   • Time hiking: 5 hours
   • Break time: 2 hours
   • Time driving home: 30 minutes = 0.5 hours
   • Total time = Time hiking + Break time + Time driving
   • Total time = \( 5 + 2 + 0.5 = 7.5 , \text{hours} \)

3. Total Distance:

   • Distance hiking + Distance driving
   • Distance driven = Speed × Time = \( 60 , \text{mph} \times 0.5 , \text{hours} = 30 , \text{miles} \)
   • Total distance = Distance hiking + Distance driving = \( 15 + 30 = 45 , \text{miles} \)

4. Average Speed Calculation:

   • Average speed = Total distance / Total time
   • Average speed = \( \frac{45 , \text{miles}}{7.5 , \text{hours}} = 6 , \text{mph} \)

Thus, the average speed of Pooja's entire trip, including her break, is 6 mph.