2. One day it began to snow at noon at a steady rate. A snowplow left its garage

ID: 2837365 • Letter: 2

Question

2. One day it began to snow at noon at a steady rate. A snowplow left its garage at 1pm

and proceeded to plow a long straight highway at a speed inversely proportional to the

depth of the snow. By 2pm it had traveled 5 miles. At 2pm, a second identical plow left

the same garage and went down the same highway as plow 1, again plowing as fast as

possible. Eventually, plow 2 overtakes plow 1 and they crash. When did this occur?

For clarity, let the position of plow 1 be designated by x(t) and the position of plow 2 be

designated by y(t).

let the rate of snowfall be r m/hr.

depth of the snow will be :d = r*(t+1). (t taken from 1PM)

speed of plow 1 = constant/ d

let the starting point be x=0.

at t=1, (2PM)

x(1)= 5 miles.

y(1)=0;

now we have to find t when x(t)=y(t).

after 2 PM , speed of plow1 = constant/(2r)

whereas speed of plow2=constant/(1r)

so, plow2 is travelling twice as fast as plow1.

at t,

5+(speed of plow1)*(t -1) = speed of plow2*(t-1)

speed of plow2=2*speed of plow1.

speed of plow1 = 5miles/hour.

so, t=2.

that is , they will crash at 3PM.

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