One morning it starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time.
If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?
The snow started at 5:30 AM. Since the plow covered twice as much distance in the first hour, we can infer that the average snow depth in the second hour is twice as deep as in the first hour.
So if we let d = depth of snow at 6:00 AM, and r = rate of snow fall per hour, then the depth of the snow after at 7:00 AM is d+r, and the depth of the snow at 8:00 AM is d+2*r.
Average snow depth between 6:00 AM and 7:00 AM is then
(d+d+r)/2
Average snow depth between 7:00 AM and 8:00 AM is
(d+r+d+2*r)/2.
Our equation then is:
2*(d+d+r)/2 = (d+r+d+2*r)/2
Solving we get d = r/2.
We conclude that snow had fallen for one half hour before the plow started at 6:00 AM.
let it snow, let it snow
