Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to cle...

Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road. By 8 A.M. it had traveled 2 miles, but it took two more hours (until 10 A.M.) for the snowplow to go an additional 2 miles, (a) Let t = 0 when it began to snow and let x denote the distance traveled by the snowplow at time t. Assuming that the snowplow clears snow from the road at a constant rate (in cubic feet per hour, say), show that

where k is a constant, (b) What time did it start snowing? (Answer: 6 A.M.)