Question
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 derive home in 30 minutes at a speed of 60 miles per hour. What was the average speed of pooja’s entire trip(including the break)
Answers
Answered by
GPT-4o mini
To calculate Pooja's average speed for her entire trip, we need to consider the total distance she traveled and the total time for the entire trip, including the break.
### Step 1: Calculate the distance Pooja hiked
Pooja hiked for 5 hours at a speed of 3 mph.
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 3 \text{ mph} \times 5 \text{ hours} = 15 \text{ miles}
\]
### Step 2: Calculate the time spent in the car
Pooja’s mother picked her up, and they drove home for 30 minutes at a speed of 60 mph. First, convert the 30 minutes into hours:
\[
30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours}
\]
### Step 3: Calculate the distance traveled in the car
Using the speed and time, we can find the distance they traveled in the car:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 60 \text{ mph} \times 0.5 \text{ hours} = 30 \text{ miles}
\]
### Step 4: Calculate the total distance and total time
Now we can sum the distances.
\[
\text{Total Distance} = \text{Distance hiked} + \text{Distance by car} = 15 \text{ miles} + 30 \text{ miles} = 45 \text{ miles}
\]
Next, we need to calculate the total time spent, including the break.
- Time hiking: 5 hours
- Break: 2 hours
- Time driving: 0.5 hours
\[
\text{Total Time} = \text{Time hiking} + \text{Break} + \text{Time driving}
\]
\[
\text{Total Time} = 5 \text{ hours} + 2 \text{ hours} + 0.5 \text{ hours} = 7.5 \text{ hours}
\]
### Step 5: Calculate the average speed
Average speed is given by the total distance divided by the total time.
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
\[
\text{Average Speed} = \frac{45 \text{ miles}}{7.5 \text{ hours}} = 6 \text{ mph}
\]
Thus, the average speed of Pooja's entire trip, including the break, is **6 mph**.
### Step 1: Calculate the distance Pooja hiked
Pooja hiked for 5 hours at a speed of 3 mph.
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 3 \text{ mph} \times 5 \text{ hours} = 15 \text{ miles}
\]
### Step 2: Calculate the time spent in the car
Pooja’s mother picked her up, and they drove home for 30 minutes at a speed of 60 mph. First, convert the 30 minutes into hours:
\[
30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours}
\]
### Step 3: Calculate the distance traveled in the car
Using the speed and time, we can find the distance they traveled in the car:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 60 \text{ mph} \times 0.5 \text{ hours} = 30 \text{ miles}
\]
### Step 4: Calculate the total distance and total time
Now we can sum the distances.
\[
\text{Total Distance} = \text{Distance hiked} + \text{Distance by car} = 15 \text{ miles} + 30 \text{ miles} = 45 \text{ miles}
\]
Next, we need to calculate the total time spent, including the break.
- Time hiking: 5 hours
- Break: 2 hours
- Time driving: 0.5 hours
\[
\text{Total Time} = \text{Time hiking} + \text{Break} + \text{Time driving}
\]
\[
\text{Total Time} = 5 \text{ hours} + 2 \text{ hours} + 0.5 \text{ hours} = 7.5 \text{ hours}
\]
### Step 5: Calculate the average speed
Average speed is given by the total distance divided by the total time.
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
\[
\text{Average Speed} = \frac{45 \text{ miles}}{7.5 \text{ hours}} = 6 \text{ mph}
\]
Thus, the average speed of Pooja's entire trip, including the break, is **6 mph**.