SOLUTION: The real-life train that Joe modeled his train set after crosses a circular pond with radius of 20.5 feet. How big of a circle should Joe draw to represent this pond in his model t

Question 182406: The real-life train that Joe modeled his train set after crosses a circular pond with radius of 20.5 feet. How big of a circle should Joe draw to represent this pond in his model train set, if he is to stay consistent with the 1:12 ration?
I actually got the answer 3.4, which I think is right. It's the question after it that is confusing.
If it takes Joe's train about 7 seconds to traverse the pond in his model set, what is a good approximation of how long it would take the real-life train to cross the real pond.
I got 84.4 seconds but, again, I'm not sure if that is right.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

A 1:12 ratio would be 1" on the model represents 1' in real life. So, 20.5 feet in real life would be represented by 20.5 inches on the model.

As to the speed, if you were modeling something you would want your model to travel the model distance per unit time to match the real train's real distance per unit time. So if it takes the model 7 seconds to cross the model bridge, it should take the real train 7 seconds to cross the real bridge. Which really makes sense, if you think about it. The real train only has to travel 41 feet to get across the real pond. If that took a minute and a half as you suggested, that would be a mighty slow train. As it is, 7 seconds to cross 41 feet is less than 6 feet per second which is only about 4 mph.

John

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