Problem 22 · 2016 Math Kangaroo
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Logic & Word Problems
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Theo’s watch runs 10 minutes slow, but he thinks it runs 5 minutes fast. Leo’s watch runs 5 minutes fast, but he thinks it runs 10 minutes slow. They both check their own watch at the same moment. Theo thinks it is 12:00. What time does Leo think it is?
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Answer: D — 12:30
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Hint 1 of 2
Turn Theo's belief into the real time, then read Leo's watch and Leo's belief.
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Hint 2 of 2
Theo thinks 12:00 and believes his watch is 5 fast, so it shows 12:05; it is really 10 slow.
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Approach: convert beliefs to true time and back
- Theo thinks it is 12:00 and believes his watch runs 5 min fast, so his watch reads 12:05.
- His watch is really 10 min slow, so the true time is 12:15.
- Leo's watch is really 5 min fast, so it shows 12:20; Leo thinks it runs 10 min slow, so he believes it is 12:20 + 10 = 12:30.
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