A man travels from one place to another at 12 km/h and returns along the same route at 9 km/h. If the total time taken for the two way journey is 2 hours 20 minutes, what is the distance between the two places in kilometres?

Introduction / Context:

This problem is another round trip time and distance question, but here the total time is given and the distance is unknown. The man travels one way at 12 km/h and returns at 9 km/h. We must use the total time of 2 hours 20 minutes to find the one way distance between the two places. This requires forming and solving an equation using time = distance / speed.

Given Data / Assumptions:

• Speed going = 12 km/h.
• Speed returning = 9 km/h.
• Total time for going and returning = 2 hours 20 minutes.
• 2 hours 20 minutes = 2 + 20/60 = 7/3 hours.
• The distance between the two places is the same each way, call it D kilometres.

Concept / Approach:

Time taken to go one way is distance divided by speed. Therefore, time while going is D / 12 and time while returning is D / 9. The sum of these two times equals the total time 7/3 hours. We then solve the equation D / 12 + D / 9 = 7/3 to find D. This is a standard algebraic manipulation of fractions and is a very common pattern in speed and time questions.

Step-by-Step Solution:

Verification / Alternative check:

Now check the times. At 12 km/h, time to cover 12 km is 12 / 12 = 1 hour. At 9 km/h, time to cover 12 km is 12 / 9 = 4/3 hours, which is 1 hour 20 minutes. Total time is 1 + 4/3 = 7/3 hours, equal to 2 hours 20 minutes, exactly matching the problem statement. This confirms that D = 12 km is correct.

Why Other Options Are Wrong:

If D were 21 km, the time going would be 21 / 12 and time returning 21 / 9, which add up to more than 3 hours. A distance of 9 km gives total time less than 2 hours 20 minutes. A distance of 35 km would produce an even larger total time. Only 12 km results in exactly 2 hours 20 minutes when using the given speeds of 12 km/h and 9 km/h.

Common Pitfalls:

Learners may incorrectly convert 2 hours 20 minutes into decimal hours, sometimes writing 2.2 instead of 2 + 20/60. Others add the speeds directly or take a simple average, which does not apply here because the distances are the same but speeds and times differ. Mismanaging fractions while adding D / 12 and D / 9 is also common. Keeping calculations clear and step by step prevents these errors.

Final Answer:

The distance between the two places is 12 kilometres.