## ranyai12 2 years ago A Michigan student is driving southeastward (passing Ann Arbor) at a speed of 45 miles/h and measures a temperature rise of 1 K/h. In addition, we observe that the air at a point 80 miles west-north-west (WNW) of Ann Arbor is 4 °C colder than in Ann Arbor. Assume that the temperature varies linearly in the WNW direction. What is the local temperature change in Ann Arbor?

1. whpalmer4

Okay, so the driver is going 45 miles every hour. The temperature rises 1 K/h, so every 45 miles, it rises 1 K, right?

2. ranyai12

right

3. whpalmer4

we can think of this as a line where the slope is 1K/45 miles, the x-value is the distance from that spot 80 miles WNW of Ann Arbor

4. whpalmer4

in fact, the assumption that the temperature varies linearly invites that very thought, because any linear equation can be written as y = mx + b, by definition, really

5. ranyai12

i thought youd have to use the equation dT/dt=DT/Dt=-U*gradientT

6. whpalmer4

I'm still a little confused about the question here, though...

7. ranyai12

8. whpalmer4

what's the context of this question (what class)?

9. ranyai12

calc 3

10. ranyai12

and its discusing dynamics

11. whpalmer4

hmm...I think I'm going to have to bow out, I'm not confident at this point that I understand the question. sorry! at first it looked like this was just a simple application of slope of a line problem...

12. ranyai12

its ok thanks for trying though!