Chapter 9, Problem 8P

Snow began to fall during the morning of February 2 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 pm but only 3 km from 1 pm to 2 pm. When did the snow begin to fall? [Hints: To get started, let 1 be the time measured in hours after noon; let x(t) be the distance traveled by the plow at time t; then the speed of the plow is dx/dt. Let b be the number of hours before noon that it began to snow. Find an expression for the height of the snow at time t. Then use the given information that the rate of removal R (in m³/h) is constant.]