Brain Teasers
Hickory Dickory Dock, the Spider Went Round the Clock...
At exactly six o'clock, a spider started to walk at a constant speed from the hour hand anticlockwise round the edge of the clock face. When it reached the minute hand, it turned round (assume the turn was instantaneous) and walked in the opposite direction at the same constant speed. It reached the minute hand again after 20 minutes. At what time was this second meeting?
Answer
First, we set up the equation for the time (t) that the spider meets the minute hand the first time. The minute hand moves at 6 degrees per minute, and the spider moves at x degrees per minute. Since the spider starts at the 6 or at 180 degrees away from the minute hand,6(t) = 180 - x(t)
Now if we say that the spider and minute hand are at the same spot, and start moving in the same direction, and the spider laps the minute hand (360 degrees plus the distance traveled by the minute hand, or 360 + 6(20) or 480 total degrees) then the distance traveled by the spider in 20 minutes must be 480 degrees. The spider, therefore, travels 24 degrees per minute.
Plug 24 degrees per minute into the equation for x, and solve:
6(t) = 180 -24(t)
6(t) + 24(t) = 180
30(t) = 180
t = 6
So the first meeting is at 6 minutes after 6, or 6:06. 20 minutes later at the second meeting is 6:26.
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Comments
Taking a more "visual" approach: clearly the second event shows that the spider is moving 4x as fast as the minute hand (which your explanation also shows).
From that fact alone, he first meets the hand 80% of the way up the clock - or at 66 as you said. This quickly yields the 6:26 answer - equivalent with your equation approach.
Thanks.
From that fact alone, he first meets the hand 80% of the way up the clock - or at 66 as you said. This quickly yields the 6:26 answer - equivalent with your equation approach.
Thanks.
I agree with tpg76. It is waste of effort to transform each one-sixtieth of the clock's circumference into six degrees. Whether you call that one-sixtieth a 'tik', a 'minut' or one minute's distance, you get the right answer without using two steps for conversions.
I liked it, but I kind of find it hard to believe that it took the spider a longer time to travel the same distance. So I think that you would have to calculate the speed of the spider in to the equation. Then again, what do I know? Good teaser.
so anticlockwise is the same as counterclockwise right?
good teaser but an exercise 4 my lazy brain
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