Re: math problem/freeways (fwd)

[Frederick Lemmerhirt <flemmerhirt@MAIL.WCC.CC.IL.US>]

> 1)  The story indicated that the present six-lane road  ( I-25 )  can carry
>  256,000  vehicles a day 'if it is not widened.'  Is this reasonable?
>
> Let's do some arithmetic.  This is approximately  43,000  cars per lane
> each day, or an average of about  1780  cars per lane for each of the  24
> hours in a day.  This is about one car every  2  seconds in each of six
> lanes. One can imagine cars at this density during the rush hours, but it
> is hard to imagine this density  24  hours a day.  Have I made a mistake or
> are the numbers wrong in the story?

This could be interpreted several ways.  Maybe this means 256,000
vehicles passing a given line across all 6 lanes.  If "rush hour" means
cars at 10m intervals traveling at 25m/s, then cars pass at the rate of
2.5/s, or 15/s for 6 lanes, or 54,000/hr.  At this rate it would take
only 5 hours of rush hour per day to account for the entire 256,000.
(10m intervals at 55mi/hr may be unsafe, but I'm afraid it's not
uncommon.)

Or maybe it means that during 24 hours 256,000 vehicles enter this
stretch of 6-lane road.  If 100,000 of these vehicles are "through
traffic", that leaves 156,000/24hr or about 1.8/s to merge in from all
the entrance ramps along this stretch of road.  If there were only 18
entry points (9 in each direction), that would mean an average of one
every ten seconds at each ramp, which doesn't seem excessive.

Are there any mistakes or unreasonable assumptions here?


Fred Lemmerhirt