Re: Math ?? non poker
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Can someone help?
Charlie was crossing a narrow bridge. When he was halfway across he saw a car on the opposite side 200 yards away and heading toward him. He turned back and ran and barely made it before the car hit him. If Charlie had tried to cross the bridge the truck would have hit him 3 yards before he reached the end. How long is the bridge?
As near as I can figure there are 5 variables- the rate of the truck and Charlie and the time it takes for both of them to get whereever they are going and then the length of the bridge.
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Ok, I am reading this as 200 yards from Charlie, not 200 yards from the other side of the bridge.
So, lets call half the bridge's length L, Charlie's speed R1 and the Car's speed R2.
Now, the distance between Charlie and where he will get hit if he goes forwars is L - 3. The relative rate of Charlie and the car here is R1+R2.
Charlie and the car meet up L away from Charlies position the other way, and their relative rate is R2-R1.
I think we need times too, but these should cancel somewhere (I'm working this out as I go). Let's call the running toward the car time T1, and the running away from the car time T2.
So now we know (R1+R2)T1 = L - 3 and (R2-R1)T2 = L.
That sais that R1T1 + R2T1 + 3 = L and R2T2 - R1T2 = L so....
T1 = (L-3)/(R1+R2) and T2 = L/(R2-R1)
We know that there is some multiple A such that T2=A*T1.
A turns out to be (LR2-LR1-3R2+3R1)/(LR1+LR2). Now we can get rid of T2.
Now we get (if I haven't screwed up the algebra)
T1*(R1+R2+3/T1) = A*T1*(R2-R1) ==> R1 + R2 + 3/T1 = A*(R2-R1)
This algebra is just getting hairy. I believe you have all the information you need to solve this but a simple way to solve it escapes me at the moment. The general attack is to find the relationship between R1 and R2, then substitue in for one of them and find L. I could be wrong, you may need another bit of info, but it feels like you have enough.
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