The fly and train math problem

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In summary, the problem is about two trains traveling towards each other on the same track, with a fly flying back and forth between them until they collide. The question is how far the fly travels until the collision. The trains will meet in five hours, so the fly will travel 150 miles in that time. Mathematically, the distance traveled can be calculated using the integral function. This problem is also a famous anecdote involving mathematician John von Neumann, who immediately answered the question with the correct distance, surprising the person who posed the problem. Most people try to solve the problem using infinite series, but von Neumann saw a simpler solution.
  • #1
camilus
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Ok so the problem:

2 trains are 100 miles apart traveling towards each other on the same track. Each train tavels at 10 miles per hour. A fly leaves the first train heading towards the second train the instant they are 100 miles apart. The fly travels at 30 miles per hour (relative to the ground not relative to the train he left). When the fly reaches the second train, it turns and heads back to the first train at 30 miles per hour (assume that the change in direction takes zero time). when the fly reaches the first train, he turns again. this process continues with the fly zipping back and forth between the trains as they come ever closer, until the two trains colide.

The question: How far does the fly travel until he is crushed? (total distance traveled not displacement from original position)
 
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  • #2
Why don't you figure out how long it takes for the trains to meet?
 
  • #3
It's also a famous anecdote
When this problem was posed to John von Neumann, he immediately replied, "xxx miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."
"You mean there's another way?" says von Neumann!
 
  • #4
daveb said:
Why don't you figure out how long it takes for the trains to meet?

Well the trains will meet in five hours so if the fly flies continuously for five hours, at 30mph, he travels 150 miles.

mathematically,

[tex]d=\int \limits_0^5 30~dx=30\int \limits_0^5 ~dx = 30[x]\limits_0^5 = 30[5-0] = 150 miles[/tex]
 
  • #5
Very good!
 
  • #6
mgb_phys said:
It's also a famous anecdote
When this problem was posed to John von Neumann, he immediately replied, "xxx miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."
"You mean there's another way?" says von Neumann!
When I first heard this problem many years ago that how I did it. I however also realized the infinite geometric approach but it is too computational. I do not find this to be challenging problem and I am sure most will agree.
 
  • #7
The way I heard it after hearing the problem, Von Neuman had the answer immediately.

"Wonderful! You must have seen the simple way! Most people take forever trying to sum the infinite series!"

"But I used infinite series."
 
  • #8
Robert, that had already been told, even in this thread! I'm getting a little tired of it.
 
  • #9
i did it the ugly way too the first time :(
 

1. What is "The fly and train math problem"?

The fly and train math problem is a classic math problem that involves calculating the distance and time it takes for a fly to travel between two moving objects, a train and a flyswatter.

2. How does the problem work?

The problem assumes that a train is traveling at a constant speed of 60 miles per hour and that a fly is flying at a constant speed of 80 miles per hour. The fly starts at the front of the train and flies towards the back where a flyswatter is waiting to catch it. The question is: how far does the fly travel before it is caught?

3. What is the formula for solving this problem?

The formula for solving this problem is distance = rate x time. In this case, we can use this formula to calculate the distance the fly travels by multiplying the fly's speed (80 mph) by the time it takes for the fly to be caught. The time can be calculated by dividing the distance between the train and the flyswatter (the length of the train) by the combined speed of the train and the fly (60 mph + 80 mph).

4. Can this problem be solved using different units of measurement?

Yes, this problem can be solved using different units of measurement as long as the units are consistent. For example, we can use kilometers and hours instead of miles and hours to solve the problem. The key is to make sure that the units of measurement for distance and speed are the same.

5. What is the answer to this problem?

The answer to this problem is that the fly will travel a distance of 160 miles before being caught by the flyswatter. This can be calculated by plugging in the values of 80 mph for the fly's speed and 60 mph for the train's speed into the formula: 160 miles = (80 mph + 60 mph) x time. Therefore, the fly will travel for 2 hours (160 miles / 80 mph) before being caught.

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