Topic: Math Puzzle (Read 2350 times)

toasty0 · « **on:** April 24, 2009, 11:20:44 pm »

Two trains race toward each other on a railway segment that’s 100 miles long. The trains are
traveling at 100 mph. A mosquito flying at 200 mph flies from one train toward the other,
and as soon as it arrives at the other train, it flips its direction and flies back toward the first
train. The mosquito continues bouncing back and forth between the trains until the trains
crash. What’s the total distance that the mosquito covers until the moment of the crash?

marstone · « **Reply #1 on:** April 24, 2009, 11:47:27 pm »

Quote from: toasty0 on April 24, 2009, 11:20:44 pm

Two trains race toward each other on a railway segment that’s 100 miles long. The trains are
traveling at 100 mph. A mosquito flying at 200 mph flies from one train toward the other,
and as soon as it arrives at the other train, it flips its direction and flies back toward the first
train. The mosquito continues bouncing back and forth between the trains until the trains
crash. What’s the total distance that the mosquito covers until the moment of the crash?

got a guess, will hold off posting it as I don't want to influance others if I am right or not.

marstone -64-

Czar Mohab · « **Reply #2 on:** April 25, 2009, 12:41:09 am »

I also have a "guess", and I want my answer to be posted, right or wrong

:

Assuming both trains are at 100mph as they pass their respective sides of the strip (mile "0" and "100", respectively);
Assuming that the skeeter can go 200mph and snap turn;
Assuming no other variables: 100 miles.

Czar "easier than I thought if I'm right" Mohab

P.S. Skeeters suck and can't fly that fast, so the "real world" answer (assuming two trains on a collision course at 100mph 100 miles from each other) is that it hits the windshield of the closest locomotive and rides the train for 50 miles.

Sarek · « **Reply #3 on:** April 25, 2009, 12:45:09 am »

I agree, 100 miles. The trains crash in a half hour and the mosquito can fly 100 miles at 200 mph in a half hour.

marstone · « **Reply #4 on:** April 25, 2009, 01:50:56 am »

well, that is what I got also, the number after my name is in hex.

My son gave the real world answer also, dead skeeter right at the start.

Tus-XC · « **Reply #5 on:** April 25, 2009, 02:09:28 am »

Quote from: Sarek on April 25, 2009, 12:45:09 am

I agree, 100 miles. The trains crash in a half hour and the mosquito can fly 100 miles at 200 mph in a half hour.

to further that if you do iteravly you find that the distance the mosquitto can travel in each pass decreases by a factor of 3

first pass is 66.67
second is 22.22
thrid is 7.41
fourth is 2.47
fifth is .82
sixth is .27

if you continue the iterations out until infinity you eventually get 100. of course logicing this out works quicker than calculus

Of course i like the real world answer to... splat

Nemesis · « **Reply #6 on:** April 25, 2009, 07:10:48 am »

That robot mosquito needs better collision avoidance.

Bonk · « **Reply #7 on:** April 25, 2009, 07:40:40 am »

We are lacking initial conditions and required information.

Quote

Two trains race toward each other on a railway segment that’s 100 miles long. The trains are
traveling at 100 mph

OK, but at what position on this 100 mile segment is each train at the beginning of this scenario? i.e. How far apart are the trains initially? And at what height is this distance measured? Also, is the track level? Also, is the track straight or curved? (if curved in any dimension, please specify in detail)

Quote

A mosquito flying at 200 mph flies from one train toward the other,
and as soon as it arrives at the other train, it flips its direction and flies back toward the first
train. The mosquito continues bouncing back and forth between the trains until the trains
crash.

OK, but are the trains flat fronted or streamlined (and on what curve)? Similarly, what is the initial altitude of the mosquito? Does it remain constant? If the track is not straight, does the mosquito follow it or fly as the crow?

This is not a simple question at all.

Nemesis · « **Reply #8 on:** April 25, 2009, 08:48:41 am »

If you're going after fiddlin little details like that Bonk how could you miss asking the length of the trains?

Bonk · « **Reply #9 on:** April 25, 2009, 08:58:49 am »

Well, just take a look at the scale of the mosquito in my highly detailed technical diagram. The other question is either one of the trains a passenger train? A mosquito that size might get hungry with all that flying...

Nemesis · « **Reply #10 on:** April 25, 2009, 01:24:55 pm »

Quote from: Bonk on April 25, 2009, 08:58:49 am

Well, just take a look at the scale of the mosquito in my highly detailed technical diagram.

Obviously the robotic mosquito had to be scaled up to get the jet engine in.

NJAntman · « **Reply #11 on:** April 27, 2009, 08:35:26 am »

What is the air-speed velocity of the unladen mosquito and is it African or European?

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