Question: travaling at $80$km/h going from $(32.5, 35.48)$ to $(27.03, ?)$ how long would it take
1. **State the problem:**
We need to find how long it takes to travel at a speed of $80$ km/h from the point $(32.5, 35.48)$ to the point $(27.03, 27.03)$ (assuming the second coordinate is $27.03$ as the user likely meant).
2. **Find the distance between the two points:**
Use the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
3. **Calculate the distance:**
$$d = \sqrt{(27.03 - 32.5)^2 + (27.03 - 35.48)^2}$$
$$= \sqrt{(-5.47)^2 + (-8.45)^2}$$
$$= \sqrt{29.9209 + 71.4025}$$
$$= \sqrt{101.3234}$$
$$\approx 10.07 \text{ km}$$
4. **Calculate the time taken:**
Time is distance divided by speed:
$$t = \frac{d}{v} = \frac{10.07}{80}$$
5. **Simplify the fraction:**
$$t = \frac{\cancel{10.07}}{\cancel{80}} = 0.125875 \text{ hours}$$
6. **Convert time to minutes:**
$$0.125875 \times 60 \approx 7.55 \text{ minutes}$$
**Final answer:** It will take approximately $7.55$ minutes to travel between the two points at $80$ km/h.