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Early one morning it began to snow at a constant rate. at 7 am a snowplow set off to clear a road. By 8 am it had traveled 2 miles, but it took two more hours(untill 10 am) 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

k* dx/dt=1/t ------------(1)

where k is a constant

b. what time did it start snowing?

well i do not actually understand what the part a. is asking. Is it just asking us to solve the diff eq (1) and see whether the solution function satisfies the conditions

x(1)=2, and x(3)=4? or??? If this is the case, then i am able to solve eq. (1), i actually did, and it satisfies the requirements mentioned.

As for the part b. i have no idea how to determine when it started to snow?

Any hints would be appreciated??