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?

Philip,

Your argument is correct if you considered that it is the average during the hour that counts. Thus at 7:30 it is twice as much as it was at 6:30, therefore it started at 5:30! Bravo to your brilliant reasoning.

If one would try to solve it by Algebra, then let:
t=0 when it started snowing,
t1=time (in hours) when it started plowing (6:00),
k=rate of snow fall, then
snow accumulated in the first hour (6:00-7:00)
S1=(t0+t0+1)*k/2
snow accumulated in the second hour (7:00-8:00)
S2=(t0+1+t0+2)*k/2
Since S2=2*S1,
2*(2t0+1)=(2*t0+3)
t0=1/2 (half an hour)
Thus the snow storm started at 5:30, since 6:00 is half an hour after it started.

For those interested in Calculus, it is possible to do it by Calculus too! The function is simply a straight line.

Best regards

Posted by P C on 2004-02-04 19:51:05