Stewart's Calculus offers "The Snow Plow Problem" (Page 648). It is worth playing with...along with this additional version from another resource.
Snow Plow Problem #1: Snow began to fall during the morning and continued steadily
into the afternoon. At noon a snowplow began removing snow from a road at a constant rate. The plow traveled 6 km from noon to 1 p.m. but only 3 km from 1 p.m. to 2 p.m. When did the snow begin to fall?
Snow Plow Problem #2: Three snowplows share responsibility for the same road. The speed of a snowplow is inversely proportional to the amount of snow in front of it. Sometime before noon it starts snowing. At noon the first snowplow starts plowing the road. It continues to snow (with the same intensity), and one
hour later the second snowplow starts plowing. At two o'clock the last snowplow starts plowing (all snowplows start at the same point and go in
the same direction). After some time (an hour or so) the third snowplow catches up with the second, and at the same moment the second snowplow catches up with the first. When did it start to snow?
Hint: Think differential equations and integrals...and then think them again!
Solution Commentary: Rather then discuss solutions, I suggest you look at these links: