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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 | Comment 5 of 6 |

Let d=depth of snow in inches, t=time in hours, V=speed in mph

V=50/(1+t) & d=1+t, noting that V=dx/dt, x being distance in miles=50

then substituting, dx=50/(1+t) dt

Integrating X=50=50ln(1+t), therfore ln(1+t)=1, and 1+t=e

Therefore t=answer desired=   e-1 hours

  Posted by Kenny M on 2010-09-13 20:54:41
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