A jeep travels from one place to another in 6 hours on the forward journey. On the return journey its speed is increased by 12 km/h and it takes only 4 hours. What is the distance (in km) travelled by the jeep each way?

Introduction / Context:
This question examines understanding of how distance, speed and time relate when a vehicle travels the same route at two different speeds. The jeep covers the same distance going forward and coming back, but with different speeds and times. Using these relationships, we can form an equation and compute the distance travelled each way.

Given Data / Assumptions:

• Time taken in the forward journey = 6 hours.
• Time taken in the return journey = 4 hours.
• Return speed is 12 km/h more than the forward speed.
• The distance from the starting point to the destination is the same for both journeys.

Concept / Approach:
Let the one way distance be D km. Then forward speed is D / 6 km/h and return speed is D / 4 km/h. The problem states that the difference between these speeds is 12 km/h. Setting up the equation (D / 4) - (D / 6) = 12 allows us to solve for D directly.

Step-by-Step Solution:
Let the distance between the two points be D km. Forward speed = D / 6 km/h. Return speed = D / 4 km/h. Given: return speed - forward speed = 12 km/h. So, D / 4 - D / 6 = 12. Take LCM of 4 and 6 which is 12: (3D - 2D) / 12 = 12. Therefore, D / 12 = 12. So D = 12 * 12 = 144 km.

Verification / Alternative check:
Forward speed = 144 / 6 = 24 km/h. Return speed = 144 / 4 = 36 km/h. The increase in speed is 36 - 24 = 12 km/h, which matches the given condition, and times 6 hours and 4 hours are consistent with the same distance of 144 km. So the solution is verified.

Why Other Options Are Wrong:

• 244 km, 344 km, and 444 km all give different speed differences when divided by 6 and 4 hours. None of them produce a difference of exactly 12 km/h.

Common Pitfalls:
Some learners mistakenly treat 6 hours and 4 hours as separate distances rather than the same distance. Others add the speeds instead of subtracting them to form the equation. Mismanaging the LCM or arithmetic when solving D / 4 - D / 6 = 12 can also lead to incorrect results.

Final Answer:
The distance travelled by the jeep each way is 144 km.