Solve the Bee Bicycle Challenge: Can You Beat the 30s Time Limit?

[Ian]

A math teacher gave this problem years ago when I was in High School. We had just finished a couple of hours of calculus, and there were only about three minutes left of the lesson. He gave us thirty seconds to give the correct answer, give yourself the same time, or fail.

A man rides a bicycle 100 miles between point A and point B at a constant speed of 25 mph. At the same time, a bee sitting on his handlebars begins to fly between A and B, but at a constant speed of 35 mph.
When the bee reaches point B ahead of the man, it immediately returns to meet him in-between and then continues to fly back and forth between the man and point B until the man finally reaches his destination.

How far does the bee fly in total? (ignore accelerating and deceleratating etc.)

 

[idontthinkright]

well,in my opinion, when you start calculating the numbers you are already wrong, given only thirty seconds,I suppose the numbers is just a distraction and the distance traveling from point a to b etc is totally irrevelent,and should be placing the point of reference on the bee instead of the man.
i'd say the time spent going to the man and then back would be the same completing the 100miles.(dont blame me if I am wrong,)

 

[verty]

The trick of this question is people get stuck on the information they don't have, and ignore the information they do have. Forget about the infinite series of lengths the bee flies. Look at what information you have.

1. Man: 25mph
2. A -> B: 100 miles
Therefore man takes 4 hours to reach B (100/25)
3. Bee: 35mph
4. (the pivotal one) Bee flies for same time as man = 4 hours
Therefore Bee distance = 35*4 = 140 miles.

 

[idontthinkright]

i guess vertigo's correct,i didnt complete the process of the 35*4,and i only got the concept correct X_X

 

[Hurkyl]

What could be easier than summing the infinite series?