P travels in his car and covers 2/5 part of his journey at a speed of 20 km/h, 1/8 part at 5 km/h and the remaining 19/40 part at 19 km/h. What is the average speed of the car during the entire journey?

14.3 km/h

The correct answer is Option (2) → 14.3 km/h

Step-by-Step Calculation:

To find the average speed for the entire journey, we use the formula:

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

1. Define the distances and speeds:

Let the total distance of the journey be $D$.

• Part 1: Distance $d_1 = \frac{2}{5}D$, Speed $v_1 = 20 \text{ km/h}$
• Part 2: Distance $d_2 = \frac{1}{8}D$, Speed $v_2 = 5 \text{ km/h}$
• Part 3: Distance $d_3 = \frac{19}{40}D$, Speed $v_3 = 19 \text{ km/h}$

2. Calculate the time taken for each part ($t = \frac{d}{v}$):

• $t_1 = \frac{\frac{2}{5}D}{20} = \frac{2D}{100} = \frac{D}{50}$
• $t_2 = \frac{\frac{1}{8}D}{5} = \frac{D}{40}$
• $t_3 = \frac{\frac{19}{40}D}{19} = \frac{D}{40}$

3. Calculate the total time ($T$):

$T = t_1 + t_2 + t_3 = \frac{D}{50} + \frac{D}{40} + \frac{D}{40}$

$T = \frac{D}{50} + \frac{2D}{40} = \frac{D}{50} + \frac{D}{20}$

To add these, find a common denominator (100):

$T = \frac{2D}{100} + \frac{5D}{100} = \frac{7D}{100}$

4. Calculate the Average Speed:

$\text{Average Speed} = \frac{D}{\frac{7D}{100}} = \frac{100}{7}$

$\text{Average Speed} \approx 14.2857 \dots \text{ km/h}$

Rounding to one decimal place, we get 14.3 km/h.