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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)

See The Solution Submitted by Jer    
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Solution numerical integration | Comment 1 of 6

DEFDBL A-Z
goal = 50
d = 1
spd = 50# / d
dt = 1# / 3600# / 10000
DO
  dist = dist + spd * dt
  t = t + dt
  d = d + dt
  spd = 50# / d
LOOP UNTIL dist >= goal
PRINT t * 3600; dist

finds

6185.814605709057  50.00000047703609

which indicates

6185.814605709057 seconds to traverse 50.00000047703609 miles.

That's 1 hour 43 minutes 5.8146 seconds to get 1/33 inch past the finish line.

Adding the final speed to the print statement shows the plow going at 18.39397199298262 mi/hr at that points, so the extra 0.00000047703609 miles took about 0.00009 seconds, so bring that time back to 1 hour 43 minutes 5.8145 seconds, to the nearest tenth of a millisecond.


  Posted by Charlie on 2010-09-13 13:35:52
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