Introduction / Context:
This question combines basic perimeter calculation of a square with unit conversion from km/h to m/s or metres per second. It is a common type of problem in time and distance topics that checks both geometry and speed conversion skills.
Given Data / Assumptions:
- Shape of field: square.
- Side length of the square field = 35 metres.
- Running speed of the boy = 9 km/h.
- We must find the time taken to complete one full round (one perimeter) in seconds.
Concept / Approach:
First, we compute the perimeter of the square, which is 4 times the side. Then we convert the speed from km/h to m/s or interpret distance and speed consistently. Time is always given by:
Time = Distance / Speed.
It is often convenient to express speed in metres per second when distance is in metres and time is required in seconds.
Step-by-Step Solution:
Step 1: Perimeter of the square = 4 * side = 4 * 35 = 140 metres.
Step 2: Convert speed from km/h to m/s. Use 1 km/h = 5 / 18 m/s.
Step 3: Speed = 9 km/h = 9 * 5 / 18 m/s = 45 / 18 m/s = 2.5 m/s.
Step 4: Time taken = Distance / Speed = 140 / 2.5 seconds.
Step 5: 140 / 2.5 = 56 seconds.
Verification / Alternative check:
Instead of converting into metres per second, we could convert distance into kilometres and time into hours. Distance = 140 metres = 0.14 km. Time in hours = 0.14 / 9 hour, and then convert that to seconds:
Time in hours = 0.015555..., multiply by 3600 seconds per hour gives 56 seconds, again confirming the result.
Why Other Options Are Wrong:
- 50 seconds: Corresponds to a slightly higher speed than 9 km/h.
- 52 seconds: Also implies a speed greater than the given 9 km/h.
- 54 seconds: Represents a small calculation error when dividing 140 by 2.5.
Common Pitfalls:
- Using side instead of perimeter, forgetting that the boy runs around all four sides.
- Incorrectly converting 9 km/h to m/s by using 18/5 instead of 5/18.
- Mixing units by using metres for distance and km/h for speed without conversion.
Final Answer:
The boy will take
56 seconds to complete one round of the square field.
Discussion & Comments