Pranav drives a car to his friend’s house. He drives the first 45 miles at 60 miles per hour. Then he stops for gas for 15 minutes. After getting gas it starts raining so he drives the rest of the trip at 50 miles per hour, and arrives 20 minutes later. What is Pranav’s average speed for the trip? A) 57 mph B) 37 mph C) 55 mph D) 40 mph E) 49 mph F) 52 mph G) 46 mph H) 42 mph

To find Pranav's average speed for the entire trip, we need to determine the total distance he traveled and the total time he took, including the stop for gas.

1. **First leg of the trip:**
   - Distance: 45 miles
   - Speed: 60 miles per hour
   - Time taken: \(\frac{45 \text{ miles}}{60 \text{ mph}} = 0.75 \text{ hours}\)

2. **Stop for gas:**
   - Time: 15 minutes = 0.25 hours

3. **Second leg of the trip:**
   - Speed: 50 miles per hour
   - Time taken: 20 minutes = 20/60 hours = 1/3 hours

To find the distance for the second leg of the trip, use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 50 \text{ mph} \times \frac{1}{3} \text{ hours} = \frac{50}{3} \text{ miles} \approx 16.67 \text{ miles} \]

4. **Total distance:**
   \[ \text{Total distance} = 45 \text{ miles} + \frac{50}{3} \text{ miles} = 45 + 16.67 = 61.67 \text{ miles} \]

5. **Total time:**
   \[ \text{Total time} = 0.75 \text{ hours} + 0.25 \text{ hours} + \frac{1}{3} \text{ hours} = 0.75 + 0.25 + 0.333 = 1.333 \text{ hours} \]

6. **Average speed:**
   \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{61.67 \text{ miles}}{1.333 \text{ hours}} \approx 46.27 \text{ mph} \]

Since 46.27 mph is closest to the option 46 mph, the correct answer is:

\[ \boxed{46 \text{ mph}} \]

Would you like any further details or have any questions? 

Here are 5 questions you might want to ask:
1. How do you calculate the distance traveled during the second leg of the trip?
2. Can you explain how to convert minutes to hours for time calculations?
3. What steps are involved in determining average speed?
4. How would the calculations change if the speeds were different?
5. What if there were multiple stops during the trip? How would that affect the average speed?

**Tip:** Always remember to convert all time measurements to the same unit (usually hours) when calculating speed or distance to ensure consistency.

Learn how to calculate Pranav's average speed for his trip to his friend’s house using distance-speed-time calculations. This problem involves multiple legs of the trip, including a stop for gas, and provides a detailed step-by-step solution. Suitable for high school students studying distance-speed-time problems.

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