Problem 5 · 2008 AMC 8
Easy
Ratios, Rates & Proportions
average-speed
Barney Schwinn notices that the odometer on his bicycle reads 1441, a palindrome, because it reads the same forward and backward. After riding 4 more hours that day and 6 the next, he notices that the odometer shows another palindrome, 1661. What was his average speed in miles per hour?
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Answer: E — 22 mph.
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Hint 1 of 2
"Palindrome" is just flavor — all you need is the two odometer readings and the total hours.
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Hint 2 of 2
Average speed always means total distance ÷ total time, no matter how the trip was split up.
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Approach: total distance ÷ total time
- Distance is just how far the odometer moved: 1661 − 1441 = 220 miles. Don't be distracted by the palindrome story.
- Total time is 4 + 6 = 10 hours, so average speed = 220 ÷ 10 = 22 mph.
- Why this transfers: average speed is never the average of two speeds — it's always all the miles over all the hours.
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