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First-Order Differential Equations

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January 25th, 2023

Two Snowplows – Differential Equations (First-Order Differential Equations)

One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00pm, and another one followed in its tracks at 2:00pm.

a)At what time did the second snowplow crash into the first? To answer this question, assume that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth of the snow (and hence to the time elapsed since the road was clear of snow). [Hint: begin by writing differential equations for x(t) and y(t), the distance traveled by the first and second snowplows, respectively, at t hours past noon. To solve the differential equation involving y, let t rather than y be the dependent variable]

b)Could the crash have been avoided by dispatching the second snowplow at 3:00pm instead?

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