Vipin travels one-third of the distance of a journey at a speed of $30 ext{ km/h}$ and the remaining distance at a speed of $40 ext{ km/h}$. If he took a total of $12$ hours to complete the journey, what was the total distance (in km) of the journey?

Question

Vipin travels one-third of the distance of a journey at a speed of $30 	ext{ km/h}$ and the remaining distance at a speed of $40 	ext{ km/h}$. If he took a total of $12$ hours to complete the journey, what was the total distance (in km) of the journey?

Accepted Answer

**Solution:**

1. Let the total distance be $3x$ km.

2. Distance covered at $30 	ext{ km/h}$ is $x$ km, and distance covered at $40 	ext{ km/h}$ is $2x$ km.

3. Time taken to cover first part:
   $$t_1 = \frac{x}{30}$$

4. Time taken to cover second part:
   $$t_2 = \frac{2x}{40} = \frac{x}{20}$$

5. Total time given is $12$ hours:
   $$t_1 + t_2 = 12$$
   $$\frac{x}{30} + \frac{x}{20} = 12$$

6. Find common denominator and solve:
   $$\frac{2x}{60} + \frac{3x}{60} = 12$$
   $$\frac{5x}{60} = 12$$
   $$5x = 720$$
   $$x = 144$$

7. Total distance:
   $$3x = 3 	imes 144 = 432 	ext{ km}$$

**Answer:** $432$

Answer

Answer

Answer