Traffic-related math question

[Aeyyyyyy]

El Fonz likes to drive fast, but he doesn't like to think. Perhaps the other actuarials will do the thinking for him? :guitar:

Let's say the Fonz travels at a constant speed of X mph, while everyone else drives a constant speed of Y mph where Y is less than X. He is driving down a long, straight 100 mile road with a stop light every 5 miles. The stop lights alternate between red and green in some manner similar to how normal stop lights alternate.

What's the relationship between Fonz's extra speed (X - Y) and the time he saves by driving faster? In other words, how do the stop lights play in? Do they...

a.) Make his expected travel time longer than if there were no stop lights?
b.) Make his expected travel time shorter than if there were no stop lights?
c.) Have no effect on the expected travel time, just increasing variance?

Aeyyyyyy! :tup:

[jimbob]

I'll assume that:

the Fonz is Red-Green color blind therefore does not stop at red lights
the Fonz incurs no penalty for not stopping
traffic does not impede his travel
has enough gas to complete the journey without stopping
does not pick up hitchhikers
is not carjacked
does not get a flat tire
waits until the end of the journey to eat/drink/toiletSo, c?

[Mark Cavazos]

If the lights are timed to someone going 100 mph, then he will make it without stopping.

Assuming that they are not: if his speed immediately drops to zero at a red light, then he will go flying through the windshield. He will never finish the trip.

[Animal]

When the Fonz snaps his fingers, all lights turn green. So assuming he utilizes this, the traffic lights will have no effect.

[Alto Reed on a Tenor Sax]

There....are.....FOUR.......lights......


http://www.livejournal.com/userpic/26284366/6179328
http://fishingjunk.com/wp-content/fourlights.png


Ummm.....or am I thinking of a different TV show rerun?

[Klaymen]

At some point, the Fonz will get through a lights that the others must stop for, and at some point those people will not catch up.

[tymesup]

At some point, the Fonz will get through a lights that the others must stop for, and at some point those people will not catch up.

Not necessarily. Suppose he misses all the lights and someone else driving at the synchronized speed makes them all.

I once drove most of Nassau County on Merrick Road at 29 mph, making all the lights (there wasn't much traffic). Going faster wouldn't have helped my time. These days, it may not be worth pissing off the other drivers, though.

[4sigma]

Fonz does not drive fast. Fonz is not in a hurry, especially with his arm around the chick in the passenger seat. Fonz drives up Mulholland Drive to "inspiration point" where there are no traffic lights.

[mr.c]

There....are.....FOUR.......lights......

:clap:

[Pseudolus]

Where do the sharks come in?

[Dr T Non-Fan]

You should check the cycles of each of the 20 (21?) traffic lights, and set your speed between each based on the patterns you have observed.

Some lights might not be set on a particular pattern. Some might be tripped based on waiting cars. This could help you (if a car is stopped in front of you), or hinder you (a car going perpendicular to you causes your light to go red).

[Chubbs]

FIRST SERIOUS ATTEMPT TO ANSWER QUESTION


We need to know fonz's acceleration. Assume car Y is at full speed and fonz is at a standstill. They both leave the starting line at the same time. Since the lights are 5 miles apart, is it reasonable to assume that Fonz will at least reach the next light at the same time as car Y? Let us assume that it is reasonable. If that light is green, than fonz will overtake car Y. If that light is red, then both vehicles must begin from a standstill and Fonz will quickly overtake car Y before the next light. It is now clear that fonz will have a shorter expected travel time.

[Dr T Non-Fan]

Also note that it's easy to time lights if you keep your eye on them a mile ahead (45 seconds to a minute) of time. You can time it so you hit them about a second or two after they turn green.
Do note the danger of this tactic: the red-light speeder-upper going perpendicular to you.

[Aeyyyyyy]

Aren't you guys all funny. :tup:

I was ignoring the effects of acceleration. All I was thinking was, sometimes I'll hit a red light and the slow cars catch up, negating my advantage. Other times I'll make it through a light that'll be red when they show up, increasing my advantage. Overall, which has the greater effect, if either?

I tried to think about it just now, but my brain shook like the Star Wars kid at a pie-eating contest. :( Fonz is one low-watt bulb.

Aeyyyyyy!

[tometom]

What's the relationship between Fonz's extra speed (X - Y) and the time he saves by driving faster? In other words, how do the stop lights play in? Do they...

a.) Make his expected travel time longer than if there were no stop lights?
b.) Make his expected travel time shorter than if there were no stop lights?
c.) Have no effect on the expected travel time, just increasing variance?a. is the obvious answer. Let's ignore the other drivers right now and just take Fonz going 50 mph. Without lights, it would take him 2 hours to reach his destination. Now add lights, if he hits only 1 light, but has to come to a complete stop and wait a short period of time, that will add a couple of minutes to 2 hours. Now factor in a possiblity of 20 lights. The main thing here is what is the chance of hitting every light given a certain speed. I personally think it is pretty obvious that it would take longer with stop lights then without.

Now lets talk about someone elses thought of slowing down to make sure Fonz hits every light green. Well, this should also be obvious, slowing down to below 50 mph for even a few seconds would make the trip take less than 2 hours.

Now there are just to many factors to include other cars in the mix, but typically over a stretch of 100 miles, as long as Fonz is going at a faster speed and the lights are randomly turning red and green, sooner or later he will make more lights then the other cars. Now if the distance was shorter, say 10 miles and their was a traffic light every half a mile, there is a good chance that unless the Fonz has a tremendous acceleration advantage, that he will arrive at the destination at the same time as other cars. Then again based on the timing of the lights, he might make everyone and the other cars will get stopped at everyone.

Your scenario has to many possibilities. You would need a good assumption about stop lights and also acceleration for both Fonz and the other cars.