An algebra teacher gave his students the following problem:
"A car is travelling along a straight road at constant speed. The car passes a mile marker sign which is a two digit number "XY". One hour later it passes mile marker "YX". After one more hour it passes mile marker "X0Y" where the central digit is a zero. All numbers are in base 10".
One of the students received a paper that was smudged in one spot, making a single character of the above quoted instructions look like some other character.
When everyone in class shared their answers, this student exclaimed: "Hey, compared to the answers you all got, my mile marker signs all look upside down, and the speed I got was 8/3 times too fast!"
Part 1. List all three signs and the speed of the car in miles per hour.
Part 2. What character was changed, and what was it changed to?
Part 1: Since the car is traveling at a constant speed, we have (100x + y) - (10y + x) = (10y + x) - (10x + y).
This simplifies to 6x = y, so x = 1 and y = 6.
Therefore the three mile marker signs were 16, 61, and 106. The car was traveling at a speed of 45 mph.
Part 2: The character that was changed was the 0 in "base 10" - it was changed to a 6, making the final line of the puzzle read "All numbers are in base 16."
With this reading, the student arrived at a solution of mile marker signs 19 (25 in base 10), 91 (145 in base 10) and 109 (265 in base 10). These result in a speed of 120 mph, 8/3 times the correct answer.
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Posted by tomarken
on 2021-07-08 08:34:29 |
Solution
