A man walking at a constant speed of 5 km/h crosses a bridge in 15 minutes. What is the length of the bridge in metres?

Introduction / Context:
This question is a simple time and distance problem involving a person crossing a bridge at a known constant speed. The key is to correctly convert time into hours and then apply the basic formula relating distance, speed and time. Because the answer is required in metres, we must also convert the final distance from kilometres to metres.

Given Data / Assumptions:

• Walking speed of the man = 5 km/h.
• Time taken to cross the bridge = 15 minutes.
• We need to find the length of the bridge in metres.
• The man walks at a uniform speed during the crossing.

Concept / Approach:
The fundamental relation is:
Distance = Speed * Time.
However, speed is given in kilometres per hour, while time is given in minutes. We must convert time from minutes to hours before using the formula, and then convert the resulting distance from kilometres to metres using 1 km = 1000 metres.

Step-by-Step Solution:
Step 1: Convert time from minutes to hours. Time = 15 minutes = 15 / 60 = 0.25 hour. Step 2: Speed = 5 km/h. Step 3: Distance in kilometres = Speed * Time = 5 * 0.25 = 1.25 km. Step 4: Convert 1.25 km to metres: 1.25 * 1000 = 1250 metres. Step 5: Therefore the length of the bridge is 1250 metres.
Verification / Alternative check:
Alternatively, convert speed to metres per minute. Speed 5 km/h = 5000 metres per hour. Per minute, this is 5000 / 60 ≈ 83.33 metres per minute. In 15 minutes, distance covered is 83.33 * 15 ≈ 1250 metres. This matches the previous calculation and verifies the answer.

Why Other Options Are Wrong:

• 600 m: Implies an effective speed of only 2.4 km/h, inconsistent with the given 5 km/h.
• 750 m: Gives an incorrect conversion and does not match distance = 5 * 0.25 km.
• 1000 m: Would correspond to a shorter time than 15 minutes at 5 km/h.

Common Pitfalls:

• Forgetting to convert minutes to hours when using km/h for speed.
• Converting distance incorrectly by using 100 instead of 1000 when moving from km to metres.
• Using 15/100 instead of 15/60 in the time conversion step.

Final Answer:
The length of the bridge is 1250 m.