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Top Hat
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A marching troop - that is, rows of soldiers walking forward in a straight line - is 25 metres long (from the first soldier at the front to the last soldier at the back). It is marching at a constant speed of 1 metre per second.

The regimental dog (located at the heel of the last soldier) runs forward from the last soldier to the first soldier. When it reaches the first soldier it turns round and runs back to the last soldier. By the time it finishes this run, the troop has moved forward by exactly 25 metres.

Assuming no acceleration or deceleration of the dog, what is the dog's speed?
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Time is 25 seconds
Let speed of dog =x
Dogspeed relative to line is x-1 on the way up and x+1 on the way back

25=25/x-1 + 25/x+1
0=x^2 -2x -1
Quadratic. I get this:
Dog speed=2.4142135 mps
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