A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

224 km

The total time required to cover the entire journey is 10 hours.

We know that, Speed = \(\frac{Distance }{Time }\),

Time = \(\frac{Distance}{Speed}\).

Let total distance traveled be x, so half of the distance traveled be \(\frac{x }{2 }\)

t₁ + t₂ = 10 hours

\(\frac{\text{Distance_1}}{\text{Speed_1}}\) + \(\frac{\text{Distance_2}}{\text{Speed_2}}\) = 10 hours

\(\frac{\frac{x}{2 }}{21}\) +  \(\frac{\frac{x}{2 }}{24}\) = 10 

\(\frac{x }{ 42}\) + \(\frac{ x}{48 }\) = 10

\(\frac{{90x}}{\text{42 × 48}}\) = 10

x = \(\frac{42 × 48 × 10}{90}\)

x = 224km