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?

P covers his journey in three parts at different speeds. Average speed is calculated as Total Distance ÷ Total Time.

Assume the total journey = 120 km (chosen as the LCM of 5, 6, and 40 to avoid decimals).

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Part 1: $\dfrac{2}{5}$ of journey

Distance $= \dfrac{2}{5} \times 120 = 48$ km

Part 2: $\dfrac{1}{8}$ of journey

Distance $= \dfrac{1}{8} \times 120 = 15$ km

Part 3: Remaining portion

Remaining $= 1 - \dfrac{2}{5} - \dfrac{1}{8}= \dfrac{19}{40}$

Distance $= \dfrac{19}{40} \times 120 = 57$ km

Total Distance $= 48 + 15 + 57= 120$ km

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Time for each part using Time $= \dfrac{\text{Distance}}{\text{Speed}}$:

Part 1: Time $= \dfrac{48}{20} = 2.4$ hours

Part 2: Time $= \dfrac{15}{5} = 3$ hours

Part 3: Time $= \dfrac{57}{19} = 3$ hours

Total Time $= 2.4 + 3 + 3 = 8.4$ hours

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

$= \dfrac{120}{8.4}\approx 14.28$ km/h (option 2).