Myra cycles to a friend's house 5 km away to deliver a packet. She goes at a speed of 12 km/hour and returns at a speed of 8 km/h. Her average speed during the whole trip is

Question

Accepted Answer

To determine Myra's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken for the trip.

1. **Total Distance:**
   - Myra cycles to her friend's house and back, so the total distance is twice the one-way distance.
   - One-way distance = 5 km
   - Total distance = 5 km (to the friend's house) + 5 km (return) = 10 km

2. **Total Time:**
   - Time taken to travel to the friend's house = Distance / Speed = 5 km / 12 km/h = 5/12 hours
   - Time taken to return = Distance / Speed = 5 km / 8 km/h = 5/8 hours
   - Total time = (5/12) hours + (5/8) hours
   - To add these, find a common denominator (24):
     - (5/12) hours = (5 * 2) / 24 = 10/24 hours
     - (5/8) hours = (5 * 3) / 24 = 15/24 hours
   - Total time = (10/24) + (15/24) = 25/24 hours

3. **Average Speed:**
   - Average speed is calculated as Total Distance / Total Time
   - Average speed = 10 km / (25/24) hours = 10 km * (24/25) = 240/25 km/h = 9.6 km/h

Therefore, the average speed for the entire trip is 9.6 km/h, which corresponds to Option 2.

**Explanation for Incorrect Options:**

1. **Option 1: 20 km/h**
   - This option is incorrect because it does not take into account the different speeds for the two parts of the journey. The average speed cannot be simply the arithmetic mean of the two speeds (12 km/h and 8 km/h) because the time spent at each speed is different.

2. **Option 3: 10 km/h**
   - This option is incorrect because it assumes an equal distribution of time at both speeds, which is not the case. The calculation of average speed must consider the actual time spent traveling at each speed, leading to the correct average of 9.6 km/h.

3. **Option 4: 5 m/s**
   - This option is incorrect because it is not in the correct unit for average speed in this context. Additionally, 5 m/s is equivalent to 18 km/h, which is not the correct average speed for this trip.

In conclusion, the correct average speed for Myra's entire trip is 9.6 km/h, making Option 2 the correct choice.