Monday, March 09, 2020
This Simple Riddle Almost Fooled Einstein
The old car goes a mile up the hill, and then a mile down the hill. It can only go 15 miles an hour up the hill. How fast must the car go down the hill in order to average 30 miles per hour for the entire two-mile trip? Duh, 45 miles per hour. But the explanation in this video went right over my head. Why does it matter how much time the trip takes? Why bring time into it at all? They lost me completely. Can you explain it any simpler than this guy does? (via Digg)
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3 comments:
Why bring time into it at all?
That's very much the point of the problem. At first, it looks like a simple averages problem: if the average is 30, and one of the variables is 15, what's the other variable? 45.
That would be the answer if you had two cars and were taking the average value of speed for the two cars.
In this case, the wording of the problem suggests we have been given only one constraint for the problem: the car will travel two miles. We don't realise, however, that we've also been given a second constraint, which is that the car must finish its journey in 4 minutes.
How does time come into it? Because speed is a function of both distance and time: miles per hour. If the car averages 30 mph and is constrained to travel no more than two miles, it must complete the journey within 4 minutes. That this time constraint is concealed in the wording is what makes it so insteresting.
Hope that helps.
Yeah, that does help. Thanks!
V=D/T
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