Wanna make a 100g? Solve a problem!

[2b]

So this was a simple problem presented to students in MIT.

First one to give me the correct answer and how they came up with it I'll give 100g to. But don't guess the answer isn't that complex and you can probably guess it. It's why you got it that will earn you the gold.

So here it is:

A bus runs 2 routes all day long.
From point B to point A and back and it takes 4 minutes.
After he goes from point B to point C and back and it takes 12 minutes.

(sort of like an 8! back and forth all day long.)

If you go to point B at any given point of the day. What would be the average wait time until the bus comes there?

[Jatone-Takall]

5.5minutes

There are 4 (general) possibilities.

1) You arrive at B and the bus just arrived at A. 2 minute wait.
2) You arrive at B and it just left for A. 4 minute wait.
3) You arrive at B and it just arrived at C. 6minutes.
4) You arrive at B and it just left for C. 12minutes.

The average wait time for the bus going to point A and back is 3,
(2+4)/2 = 3.

The average wait time for the bus going to point C and back is 8,
(6+12)/2 = 8

So your average wait time for any given point of the day when you get to point B is 5.5, (3+8)/2 = 5.5.

[2b]

that answer is incorrect.

the question is if you go to B at any point of the day what the wait time would be.

i'll give hints if people give up and nobody wants to try anymore.

[Klarya]

its 4 minutes...because if the bus is at point A then it will be 2 minutes for it to get to B and if its at C its 6 minutes back. So at any given time of the day theres a potential of waiting 4 minutes.

[2b]

that would be too simple 4 would be too simple

[Kobetauren]

Quick obvious guess: 8 minutes. (4/2)+(12/2)=8
But it doesn't feel right.

[Jatone-Takall]

how does the routes work, does the bus have to go to A to B to C to B to A? or can it go C to B to C to B to A?

[2b]

8 and 4 are both wrong answers

[Zenyatta25]

My guess 36 minutes.

I don't do math like the normal joe. I tend to go the long way around.

If when going in one direction Point B is the 4 minute mark point A is the 2 minute mark and going the other, Point B is the 12 minute mark, Point C is the 6 minute mark.

If when you get to the station B and the bus just left 1 minute ago on the 4 minute route, you have 3 minutes remaining. If it left 2 minutes ago there are 2 minutes remaining. And same the other direction. If you use each equal distance amounts as a 1 minute marker around his route and you lay that out you'd get...

Minute Point - Minutes Remaining
1.....................................3
2.....................................2
3.....................................1
4.....................................0
1.....................................11
2.....................................10
3.....................................9
4.....................................8
5.....................................7
6.....................................6
7.....................................5
8.....................................4
9.....................................3
10...................................2
11...................................1
12...................................0

You add up the minutes remaining column and take the average which comes to 36.

EDIT: This thing doesn't like spaces very much

[2b]

if the average wait time for going 1 way is 2 mins and going the other way is 6 mins the average is gonna be somewhere in between

[Zenyatta25]

I told you before... I DON'T DO MATH I'm too damn creative for math.

[2b]

i'm not creative at all so i do math

[Zenyatta25]

Well to come up with my conclusion like I did, I drew out little diagrams instead of mathematically figuring it out.

[2b]

i'll wait a couple of days to see if anybody can solve it or care to actually try and i'll post the answer. i don't know how many people give a shit since most people despise math.

[Songi]

Any point of the day? Is that even calculable? The Average wait time is random.

but if I was to do a math problem in my head I would guess 4.5 minutes. Average.