Average Speed Calculation Steps

To find the average speed for the entire trip, we calculate the total distance traveled and divide it by the total time taken. The formula for average speed is Total Distance / Total Time.

1. Calculate Time for Each Part

The time taken for each part of the journey is calculated using the formula: Time = Distance / Speed.

• Part 1:
  • Distance ($d_1$) = 10 km
  • Speed ($s_1$) = 12 km/h
  • Time ($t_1$) = $\frac{d_1}{s_1}$ = $\frac{10 \text{ km}}{12 \text{ km/h}}$ = $\frac{5}{6}$ hours
• Part 2:
  • Distance ($d_2$) = 12 km
  • Speed ($s_2$) = 10 km/h
  • Time ($t_2$) = $\frac{d_2}{s_2}$ = $\frac{12 \text{ km}}{10 \text{ km/h}}$ = $\frac{6}{5}$ hours

2. Calculate Total Distance and Total Time

Add the distances and times from both parts.

• Total Distance ($d_{total}$) = $d_1 + d_2$ = 10 km + 12 km = 22 km
• Total Time ($t_{total}$) = $t_1 + t_2$ = $\frac{5}{6} \text{ h} + \frac{6}{5} \text{ h}$
• Find a common denominator (30) to add the fractions:
• $t_{total}$ = $\frac{25}{30} \text{ h} + \frac{36}{30} \text{ h}$ = $\frac{61}{30}$ hours

3. Calculate Average Speed

Apply the average speed formula using the calculated totals.

• Average Speed ($s_{avg}$) = $\frac{d_{total}}{t_{total}}$ = $\frac{22 \text{ km}}{\frac{61}{30} \text{ hours}}$
• $s_{avg}$ = $22 \times \frac{30}{61}$ km/h = $\frac{660}{61}$ km/h

4. Approximate the Result

Calculate the final value and round appropriately.

$s_{avg} \approx 10.81967...$ km/h

The approximate average speed for the entire trip is 10.8 km/h.