Daily Math Puzzle: 2026-08-30

7.2 miles per hour — Let's break down Amelia's journey: 1. **Total Distance:** The supermarket is 6 miles away. So, a round trip (to the supermarket and back home) covers a total distance of 6 miles + 6 miles = 12 miles. 2. **Total Time for the Round Trip:** Amelia's average speed for the entire 12-mile round trip was 9 miles per hour. Using the formula Time = Distance / Speed, her total time for the trip was 12 miles / 9 mph = 4/3 hours (which is 1 hour and 20 minutes). 3. **Time to the Supermarket:** Amelia cycled to the supermarket (6 miles) at a speed of 12 miles per hour. Using the formula Time = Distance / Speed, the time taken for this leg was 6 miles / 12 mph = 0.5 hours (or 30 minutes). 4. **Time Back Home:** To find the time Amelia took to cycle back home, subtract the time to the supermarket from the total trip time: Time back home = Total Time - Time to supermarket Time back home = (4/3) hours - 0.5 hours Time back home = (8/6) hours - (3/6) hours = 5/6 hours (or 50 minutes). 5. **Speed Back Home:** Amelia cycled 6 miles back home in 5/6 hours. Using the formula Speed = Distance / Time: Speed back home = 6 miles / (5/6) hours = 6 * (6/5) mph = 36/5 mph = 7.2 miles per hour. Many people might instinctively try to average the two speeds (12 mph and X mph) to get 9 mph, which would incorrectly lead to 6 mph. However, average speed is always calculated as total distance divided by total time, not simply as the average of the individual speeds, especially when the times spent at those speeds are different.