To find the average speed of Pooja's entire trip, we need to calculate the total distance she traveled and the total time spent including the break.
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Distance hiked: Pooja hiked at a speed of 3 mph for 5 hours. \[ \text{Distance} = \text{Speed} \times \text{Time} = 3 , \text{mph} \times 5 , \text{hours} = 15 , \text{miles} \]
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Time spent hiking: The time spent hiking is 5 hours.
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Time spent on break: Pooja took a 2-hour break. \[ \text{Break time} = 2 , \text{hours} \]
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Time spent driving home: Pooja's mother picked her up and they drove home for 30 minutes at a speed of 60 mph. First, convert 30 minutes to hours: \[ 30 , \text{minutes} = \frac{30}{60} , \text{hours} = 0.5 , \text{hours} \]
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Total distance: The total distance for the entire trip is the distance hiked (15 miles), as the driving part is returning home and does not contribute to the displacement for calculating average speed. \[ \text{Total distance} = 15 , \text{miles} \]
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Total time: Now, add all the times together:
- Hiking time: 5 hours
- Break time: 2 hours
- Driving time: 0.5 hours \[ \text{Total time} = 5 , \text{hours} + 2 , \text{hours} + 0.5 , \text{hours} = 7.5 , \text{hours} \]
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Average speed: Finally, we can calculate the average speed over the entire trip: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{15 , \text{miles}}{7.5 , \text{hours}} = 2 , \text{mph} \]
Thus, the average speed of Pooja's entire trip is \( \boxed{2} \) mph.