## Friday, August 31, 2007

### I Got Stuck Behind a Bus This Morning

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 was it when the boy arrived at school?

1. Billy looks in the mirror, the clock looks like its at 4:35. He pedals 20 minutes to school. He thinks that its 4:55. he looks at the school clock to see that its actually 7:25

7:25-4:55=2:30

How I got this:
Clocks are circular, which makes them hard to draw and manipulate on paper. so i drew a line graph with a 6 in the middle. (probably could've done it with a 12, but my highschool starts at 7:15, so this is more appropriate). counted 1:15 in each direction, added :10 to each side to account for the 20 minute bike ride, and did the math.

[But what billy shouldve done is turned around to look at the clock the proper way, instead of thinking that it was 4:35 in the morning. or he couldv'e used that as an excuse to go back to bed for another few hours.]

2. Well, the riddle says that the time it was when he arrived was 2.5 hours after the time he thought he saw. I think you added 20 minutes to the wrong time. If the boy thought he saw 4:35, it would have actually been 7:25, making it 7:45 when he actually got to school, which is 3 hours and 10 minutes after the time the boy thought he saw.

There is a way to do this one with just equations. Assuming this is in the morning (which makes sense, since he's going to school) and so we're not crossing the 12:00 barrier, we can write the reflection (T') of the current time (T) as:

T' = 12 - T

Therefore, adding the 20 minutes (1/3) and the 2.5-hour difference,

T + 1/3 - 2.5 = 12 - T

or

T = 7.0833 = 7:05 AM

He looked in the mirror and saw 4:55, assumed the clock was broken, rode 20 minutes to school, making it 7:25 AM when he arrived, exactly 2.5 hours after 4:55.

3. abe, you're absolutely correct. I added 20 minutes in to the time that he saw in the mirror, which I'm glad you caught.

4. I believe you have figured it all out. The time difference was 2 hours and 10 minutes (after taking out the 20 minutes of riding). So, the time on the clock must have been 7:05, which when seen in a mirror would look like 4:55.

Note that also five minutes past one can be mirrored in a similar way, but this is not in the morning.

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