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### Question

You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) how far is your hometown from school? (b) What was your average speed?

### Answer #1 for Questions: You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) how far is your hometown from school? (b) What was your average speed?

This is a simple problem about **speed**, **distance** and **time**. The equation that must be used for this problem is shown below:

* Eqn 1: *[tex]v = frac{d}{t}[/tex]

To answer the first question (a), we must first identify the time [tex]t_1[/tex] taken by the car when it was running at speed [tex]v_1[/tex] of 95 km/h for a distance [tex]d_1[/tex] of 180 km.

Rearranging * Eqn 1*, we will have

[tex]t_1 = frac{d_1}{v_1} \t_1 = frac{180km}{95km/h}\t_1 = 1.895 h[/tex]

This means that the car used 1.895 hours to travel 180 km from school. Because of rain, the car slowed down to a speed [tex]v_2[/tex] of 65 km/h. Since we know that the total time [tex]t_T[/tex] used by the car to travel from school to home is 4.5 hours, we can identify the time [tex]t_2[/tex] it took to travel using a speed of 65 km/h.

[tex]t_T = t_1 + t_2\4.5h = 1.895h + t_2\t_2 = 2.605h[/tex]

Using this time [tex]t_2[/tex], we can now calculate the distance [tex]d_2[/tex] it covered from the time the rain fell up to the time it reached its home.

[tex]d _2= v_2t_2\d_2 = (65km/h)(2.605h)\d_2 = 169.325km[/tex]

Thus, the total distance from school to home is

[tex]d_T = d_1 + d_2\d_T = 180km + 169.325km\d_T = 349.325 km[/tex]

Next, to answer the second question (b), we will still use * Eqn 1 * but this time we will find the average speed [tex]v_{ave}[/tex] using the total distance [tex]d_T[/tex] and total time [tex]t_T[/tex].

[tex]v_{ave} = frac{d_T}{t_T} \v_{ave} = frac{349.325km}{4.5h} \v_{ave} = 77.63 km/h[/tex]

Therefore the final answers are:

a) **Total distance = 349.325 km**

b) **Average speed of the car = 77.63 km/h**

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