Question

Bet you can't solve this differential equation that i need help with......On a certain day it begins to snow early in the morning and the snow continues to fall at a constant rate. The velocity at which a snowplow is able to clear the road is inversely proportional to the height of the accumulated snow. The snowplow starts at 11am and clears 4 miles by 2pm. By 5pm it clears another 2 miles. When did it start snowing?

Answer 1

this is straight forward

Answer 2

Well please shed some light on me then since I don't even know how to set up my equation

Answer 3

these questions are similar to crime investigation differential equations

Answer 4

let me give hints first for encouragement

Answer 5

remember Newton's law of cooling and dead body investigation

Answer 6

this question requires a derivation of real world application

Answer 7

So then I am assuming that we need to pay attention to height of the snow, the velocity of the snowplow, time and distance?

Answer 8

ds/dt is ur rate of sonowing

Answer 9

\[\frac{ds}{dt} \alpha \frac{ ? }{ ? }\]

Answer 10

i hope this is a better clue

Answer 11

Would it be velocity of the snowplow divided by the height of the snow?

Answer 12

yes

Answer 13

u want to call the snow plow sp or s for ds its up to u to decide the names

Answer 14

so then we just have ds over dt is inversely proportional to the velocity of the snowplow divided by the height of the snow and then we would integrate both sides to get rid of the derivative? Or should i think more along the lines of moving the equation around to make it into a diffy q that I already know how to solve?

Answer 15

no integrate both side using variable separable the old terminology of diff eq

Answer 16

trust me i can see u r clever u can solve it urself, i found the answer in my head, but solve ur question and i will check the answer...

Answer 17

the only trick in this question was the snow continues to fall at a constant rate!

Answer 18

i will be back after i am done with a customer....