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