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Slowing by snowing (Posted on 2010-09-13) Difficulty: 2 of 5
A snowplow heads out to plow a 50 mile stretch of highway when there is already an inch of snow on the ground. The snow is falling steadily at a rate of one inch per hour. The speed of the plow is 50/d mph where d is the depth of the snow in inches.

How long does the plow travel this 50 mile stretch of road? (one way)

  Submitted by Jer    
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Solution: (Hide)
Pretend the snow falls discretely over x even intervals of distance plowed. (For example if x=10 after the first 5 miles takes .1 hours, .1 inch falls. Since there are 1.1 inches on the ground the next 5 miles takes an additional .11 hour so .11 inch falls etc.)

The time, in terms of x, is ((x+1)/x)^x - 1 or
t(x)=(1+1/x)^x - 1.

What is sought is the limit as x goes to infinity. Since e is defined as the limit as x goes to infinity of (1+1/x)^x the solution is e-1 or about 1.718 hours.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): numerical integration - Agree with CharlieKenny M2010-09-13 20:56:17
SolutionKenny M2010-09-13 20:54:41
re(2): numerical integrationCharlie2010-09-13 15:29:45
solution by integrationJustin2010-09-13 15:24:37
re: numerical integrationJer2010-09-13 14:52:02
Solutionnumerical integrationCharlie2010-09-13 13:35:52
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