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From: Kent Holing on 9 Aug 2010 22:31 A town has two identical cars used to clear the snow from the roads. These cars always clear the same amount of snow pr. time unit regardless the amount of snow on the ground. One day it started to snow in the late morning and it snowed steadily for the rest of the day. At noon, one of the snow cars started to clean a road. At 1 p.m, the other car started on the same route as the first car. At 2 p.m., it ran into the rear of the first car. When did it start to snow? Anybody help?
From: A N Niel on 10 Aug 2010 07:42 tIn article <727648451.85135.1281421892432.JavaMail.root(a)gallium.mathforum.org>, Kent Holing <KHO(a)statoil.com> wrote: > A town has two identical cars used to clear the snow from the roads. These > cars always clear the same amount of snow pr. time unit regardless the amount > of snow on the ground. One day it started to snow in the late morning and it > snowed steadily for the rest of the day. At noon, one of the snow cars > started to clean a road. At 1 p.m, the other car started on the same route > as the first car. At 2 p.m., it ran into the rear of the first car. When did > it start to snow? > Anybody help? What have you tried so far?
From: Kent Holing on 10 Aug 2010 06:48 It starts to snow at 12-s hour (s>0). Let the speed of car 1 be v1(t) where v1(t) a t = A for constants a and A (non-zero). This gives v1(t) = a/t since v1' a t + v a = 0. At 2 pm hour, the car 1 has travelled int(v1(t)dt)from s to s+2 = a ln((s+2)/s). Car 2 has then travelled the same distance. But how is v2(t) (the speed of car 2) related to v1(t)?
From: Robert Israel on 10 Aug 2010 10:59 Kent Holing <KHO(a)statoil.com> writes: > A town has two identical cars used to clear the snow from the roads. These > cars always clear the same amount of snow pr. time unit regardless the > amount of snow on the ground. One day it started to snow in the late > morning and it snowed steadily for the rest of the day. At noon, one of the > snow cars started to clean a road. At 1 p.m, the other car started on the > same route as the first car. At 2 p.m., it ran into the rear of the first > car. When did it start to snow? > Anybody help? Look up "snowplow problem". -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
From: Rick Decker on 10 Aug 2010 11:39
On 8/10/10 2:31 AM, Kent Holing wrote: > A town has two identical cars used to clear the snow from the roads. These cars always clear the same amount of snow pr. time unit regardless the amount of snow on the ground. One day it started to snow in the late morning and it snowed steadily for the rest of the day. At noon, one of the snow cars started to clean a road. At 1 p.m, the other car started on the same route as the first car. At 2 p.m., it ran into the rear of the first car. When did it start to snow? > Anybody help? I reviewed a paper on this topic a long time ago. As Robert implied, it's moderately well-known. I can say for sure that I wouldn't want to be anywhere nearby when the second one rear-ended the first at faster than the speed of light. Regards, Rick |