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#### Two cyclists began a training run, one starting from Moscow and the other starting from Simferopol. When the riders were 180 miles apart, a fly took an interest. Starting on one cyclists shoulder, the fly flew ahead to meet the other cyclist. After reaching him the fly then turned around and yet back. The restless fly continued to shuttleback and fourth until the pair met; then settled on the nose of one rider. The flys speed was 30 mph. Each cyclist speed was 15 mph. How many miles did the fly travel?

**Answer: ** The cyclists took 6 hours to meet. The fly traveled 6*30=180 miles.

**Solution: **

#### 2, 3, 5, 9, 17, _ What is the next number in the sequence?

**Answer: ** 33. The pattern: Double the previous number and subtract 1.

**Solution: **

#### A boy leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason, the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, the boy cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that the boy saw on the clock at home. What time is it?

**Answer: ** The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!). Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!...

**Solution: **

## Show Answer

The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!). Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!…

## Show Answer

The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!). Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!…

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