I was going to take a trip to my friend's house in San Jose by airplane. If my airplane had arrived on time as scheduled, my friend would drive out to pick me up from San Jose's airport. She would get to the ariport just as I would be leaving it, and drive me to her house. This way, I would come to her house at 12:00.

But as it happened, my airplane arrived at the airport 1 hour earlier. So I walked from the airport directly to my friend's house. On the way to her house, I met her driving to pick me up. I got into the car, and we drove me to the house. This way, I arrived at the house at 11:40.

How long did I spend walking? (The only thing known about my walking speed and my friend's driving speed is that they are different and they are constant.)

Here was my disgusting solution. The intuitive route is so much better. In fact stop reading this post.

d = distance from airport to house
gt = go-time for friend to leave house
at = normal arrival time of airplane
carsp = car speed
wd = walking distance
wt = walking time

carsp = 2*d/(12:00-gt) (distance over time)
carsp = 2(d-wd)/(11:40-gt)

at + d/carsp = 12:00
(at-1) + wt + (d-wd)/carsp = 11:40

<Why are you still reading this?>

Now substitute carsp from the first two equations into the second two and you end up with another 2:

(1) at + (12:00-gt)/2 = 12:00
(2) at-1 + wt + (11:40-gt)/2 = 11:40

Take the 1 from equation (2) over to the other side.

at + wt + (11:40-gt)/2 = 12:40

<You can't be enjoying this>

Now add and subtract twenty minutes in the bracket:

at + wt + (11:40-gt+20mins-20mins)/2 = 12:40
which equals:
at + wt + (12:00-gt)/2 + 20mins/2 = 12:40

Take the 20mins/2 or 10mins to the other side:

at + wt + (12:00-gt)/2 = 12:50

Looking at equation (1), we can see wt = 50 mins.

<You are sick>

Posted by Jack Squat on 2004-01-02 16:19:28