A man travels a certain distance at 12 km/h and returns to the starting point at 9 km/h. The total time taken by him for the entire journey is $$2 \frac{1}{3}$$ hours. The total distance (in km) covered by him is:

Let distance be x

Speed of upward journey = 12 km/hr

Speed for downward (return) journey = 9 km/hr

Total time, t = 2 hr 20 min =

$$2 + \frac{20}{60} hr = 2 + \frac{1}{3} = \frac{6+1}{3} = \frac{7}{3} hr$$

Let the distance travelled be 'x' km.

$$Speed = \frac{Distance}{Time}$$

When speed (upward journey) = 12 km/hr

Time, $$t = \frac{x  km}{12  km/hr}$$

$$= \frac{x}{12}hr$$
(ii) When speed (return journey) = 9 km/hr

Time, $$t = \frac{x  km}{9  km/hr}$$

$$= \frac{x}{9}  hr$$

Therefore, total time taken to complete the journey,

According to question

$$\frac{x}{12}$$ + $$\frac{x}{9}$$ = $$\frac{7}{3}$$

LCM of 12 and 9 is = 36

$$\frac{3x+4x}{36}$$ = $$\frac{7}{3}$$

$$\frac{7x}{36}$$ =  $$\frac{7}{3}$$

x =  $$\frac{7×36}{3×7}$$

x = 12km

So Distance= 12km

He travelled again to starting point hence = 12×2=24km