Two donkeys are standing 400 metres apart. The first donkey can run at 3 m/s and the second can run at 2 m/s. If both donkeys start running towards each other at the same time, after how many seconds will they bump into each other?

Introduction / Context:

This problem is a simple example of relative speed when two objects move towards each other. The donkeys start some distance apart and run directly towards one another at given speeds. We are asked to find how long it takes before they meet. Such questions are very common in aptitude tests and train quick reasoning with relative motion.

Given Data / Assumptions:

• Initial distance between the two donkeys = 400 metres.
• Speed of the first donkey = 3 m/s.
• Speed of the second donkey = 2 m/s.
• They start at the same time and run directly towards each other.
• They run in a straight line at constant speeds.

Concept / Approach:

When two objects move towards each other, their relative speed is the sum of their individual speeds. The distance between them decreases at this combined speed. Time taken to meet is therefore the initial distance divided by the relative speed. We simply add the two speeds, then divide the initial distance by this sum to get the meeting time.

Step-by-Step Solution:

Verification / Alternative check:

We can check by computing how far each donkey runs. In 80 seconds, the first donkey covers 3 * 80 = 240 metres and the second covers 2 * 80 = 160 metres. The sum 240 + 160 = 400 metres, exactly the initial separation. This confirms that 80 seconds is the correct time for them to bump into each other.

Why Other Options Are Wrong:

If the time were 60 seconds, the total distance covered would be (3 + 2) * 60 = 300 metres, which is not enough to close the 400 metre gap. If the time were 40 seconds, only 200 metres would be covered in total. Option 400 seconds is far too long and would correspond to a total distance of 2 000 metres at the relative speed of 5 m/s. Only 80 seconds gives exactly 400 metres, matching the initial separation.

Common Pitfalls:

Students sometimes subtract the speeds instead of adding them when the objects are moving towards each other, which is incorrect. Another error is to confuse metres per second with kilometres per hour and attempt unnecessary conversions. Remember that for motion towards each other, relative speed is the sum of speeds when they are along the same line.

Final Answer:

The donkeys will bump into each other after 80 seconds.