Calculating Average Speed for Mr. Q's Journey

To find the average speed, we need to calculate the total distance travelled and the total time taken for the entire journey. The formula for average speed is:

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $

Calculating Total Distance

Mr. Q travelled in three parts. The total distance is the sum of the distances of these parts:

• Distance 1: $336$ km
• Distance 2: $925$ km
• Distance 3: $432$ km

Total Distance ($D$) = $336 \text{ km} + 925 \text{ km} + 432 \text{ km} = 1693 \text{ km}$

Calculating Total Time

We need to find the time taken for each part of the journey using the formula $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $.

• Time 1 ($t_1$) = $ \frac{336 \text{ km}}{24 \text{ km/hr}} = 14 \text{ hours} $
• Time 2 ($t_2$) = $ \frac{925 \text{ km}}{5 \text{ km/hr}} = 185 \text{ hours} $
• Time 3 ($t_3$) = $ \frac{432 \text{ km}}{12 \text{ km/hr}} = 36 \text{ hours} $

Total Time ($T$) = $t_1 + t_2 + t_3 = 14 \text{ hours} + 185 \text{ hours} + 36 \text{ hours} = 235 \text{ hours}$

Calculating Average Speed

Now, we can calculate the average speed using the total distance and total time:

Average Speed = $ \frac{1693 \text{ km}}{235 \text{ hours}} $

To express this as a mixed number, we divide 1693 by 235:

$ 1693 \div 235 $

$ 235 \times 7 = 1645 $

The remainder is $ 1693 - 1645 = 48 $.

So, the average speed is $ 7 \frac{48}{235} $ km/hr.