Arpit completes a journey in 10 hours. He covers half of the distance at 30 km/h, and the remaining half of the distance at 70 km/h. What is the length of the journey?

Let's assume the length of the total journey is '2d' km.

Arpit completes a journey in 10 hours. He covers half of the distance at 30 km/h.

Let's assume the time taken is 't' hours when speed is 30 km/h.

$$speed=\ \frac{distance}{time}$$
$$30 = \ \frac{d}{t}$$

$$t = \ \frac{d}{30}$$    Eq.(i)

the remaining half of the distance at 70 km/h.

$$speed=\ \frac{distance}{time}$$

$$70 = \ \frac{d}{10-t}$$

$$10-t = \ \frac{d}{70}$$

$$10-\frac{d}{70} = t$$    Eq.(ii)

So  Eq.(i) =  Eq.(ii)

$$\frac{d}{30} = 10-\frac{d}{70}$$

$$\frac{d}{30}+\frac{d}{70}=10$$

the length of the total journey = '2d' km

= $$2\times210$$ km

= 420 km