Reply To: Puzzles
It has been 4 weeks now so time for the E-Bots answer.
Answer : 20 MPH
For this forum’s audience I was seeking this simplified answer.
Now before you throw your arms in the air screaming but, but, but what about. .
I will accept 20.05 as the more complex math answer.
Consider:
Speed-E travels a total distance equivalent to twice the column’s length (2 × 10 = 20 miles) in 1 hour, and the effect of the column’s motion (1 mph) cancels out due to the distance “lost” going to Head-E being balanced by the distance “gained” returning to End-E. This results in a constant speed of exactly 20 mph in the ground frame, as verified by the total distance travelled (10.5263 miles forward + 9.4737 miles back = 20 miles) in 1 hour.
The calculation yielding ( 10 + sqrt(101) approx 20.05 mph ) arises from a more complex approach that strictly accounted for Speed-E’s exact position matching End-E’s at ( t = 1 ), but my approach shows the problem intends a simplification where
- the total distance
governs the speed, making 20 mph the correct and intended answer.