(no subject)

[sereneorange]

Scooby snack for the first person who gives me the answer:

A fly is flying between two boys on bicycles who are peddling toward each other at 10 miles per hour. The fly reaches one boy, reverses immediately, and flies back to the other boy instantly, repeating the process each time. The fly is flying at 60 miles. The boys meet in thirty minutes. How far has the fly flown in that time?

Comments

[serene-orange.livejournal.com]

That is what everyone else has been getting, except Robert came up with some reason, that I now forget, why is it 30, but mathmatically impossible to come up with an exact answer. He went full on geeky with some fractions. Made sense yesterday. . .

[wakeupkent.livejournal.com]

oh you want math to support the answer! You've made the engineer in me very happy. I can do that.

First, let's convert the speeds into miles per minute.

Speed A = 1/6 mpm
Speed B = 1/6 mpm
Speed C = 1 mpm

The initial distance is 10 miles, so Object C (the fly) will meet Object B (the second boy) at 7t/6 = 10 (1/6 + 1 = 7/6), so after 8.571428571 minutes.
At that moment:
A and B have each traveled t/6, which equals 1.428571429 miles. The fly has traveled 1t, which equals 8.571428571 miles.
Calculate the distance left: 10 - 2(t/6) = 7.142857143 miles

Repeat the process. Now Object C will meet Object A (the first boy) at 7t/6 = 7.142857143. This time, t = 6.12244898. On this leg, the boys each traveled 1.020408163 miles (t/6), and the fly traveled 6.12244898 miles (1t). At the end of this leg, the distance left between the 2 boys is 7.142857143 - 2(1.020408163) = 5.102040816
miles.

I could keep going and going until the distance between the boys is infinitesimally small (though never actually 0), but let's look at the information so far:

1st meet at 8.571428571 minutes
2nd meet at 6.12244898 minutes
Add the two times together, and you'll see that 14.69387755 minutes have elapsed. The fly has, to this point, traveled 8.571428571 miles + 6.12244898 miles, for a total of 14.69387755 miles. Note how the time elapsed is equal to the distance traveled by the fly.

[eonblue21.livejournal.com]

so in my simple way of doing things, my conclusion of 15 wasnt so far off

neat :)

[wakeupkent.livejournal.com]

you were literally halfway there. :)

[wakeupkent.livejournal.com]

The reason you wouldn't get an exact answer is because at each meeting, less and less time is elapsing, at the same time that less and less distance is being covered. It really depends on how exact a calculation you want. Eventually, the fly will be traveling 1e-90 miles every 1e-90 minutes (I'm using this number as an arbitrary example), and that number will just keep getting smaller and smaller, though never actually reaching 0. It's like saying 2 boys start out standing 100 feet apart, and every 1 minute, they half the distance between themselves. At how many minutes will they meet?
A:100
B:50
C:25
D:12.5
E:6.25
F:3.125
G:1.5625
H:0.78125
I:0.390625
J:0.1953125
K:0.09765625
L:0.048828125
M:0.024414063
N:0.012207031
O:0.006103516
P:0.003051758
Q:0.001525879

at this point, the boys are standing about 1/100 of an inch away from each other, and you'd be hard pressed to be able to physically half the distance between them, but from a purely mathematical stand point, you can keep going and going to where time = infinity. The boys will never ever meet. Lovely, yes?

[serene-orange.livejournal.com]

that is so cool.

[wakeupkent.livejournal.com]

you mock me :(

[serene-orange.livejournal.com]

NO! seriously... I don't. I think it was cool.

man are you ever insecure about your nerdy abilities, you big girl.

[wakeupkent.livejournal.com]

so nerdy is cool now?

[serene-orange.livejournal.com]

is to me... but I do not exactly hold the litmus strips of cool, y'know, so you may still be a complete dork.