An industrial loom weaves 1.14 metres of cloth every second. Approximately how much time will it take to weave 52 metres of cloth at this constant rate?

Introduction / Context:
This question is a direct application of the chain rule and the unitary method in the context of speed and time. The loom weaves a certain length of cloth every second, and we need to determine how long it will take to weave a specific total length. Such questions are very common in aptitude tests and help to build comfort with division, rates, and approximations.

Given Data / Assumptions:

• The loom weaves 1.14 metres of cloth every second.
• The total length of cloth to be woven is 52 metres.
• The weaving rate is constant for the entire process.
• The final answer is to be chosen approximately from the given options.

Concept / Approach:
The relationship between distance, speed, and time is: time = distance / speed Here, distance is the total length of cloth, speed is the weaving rate in metres per second, and time will naturally come out in seconds. Since the speed is given per second, no unit conversion is needed. We simply divide 52 by 1.14 and then compare the result to the options, rounding as needed.

Step-by-Step Solution:
Weaving rate = 1.14 metres per second Required length = 52 metres time in seconds = 52 / 1.14 Compute the division: 52 / 1.14 ≈ 45.61 seconds So the loom will take approximately 45.61 seconds to weave 52 metres of cloth Among the options, 45.61 seconds matches exactly and is therefore the correct choice

Verification / Alternative check:
As a rough check, if the speed were 1 metre per second, 52 metres would take 52 seconds. Since the loom actually weaves slightly more than 1 metre per second, the time required should be somewhat less than 52 seconds. Our calculated value of about 45.61 seconds is indeed less than 52 seconds but not extremely small, so it fits this intuitive check quite well.

Why Other Options Are Wrong:
29.32 seconds and 39.25 seconds are too low and would imply a much higher weaving speed than 1.14 metres per second. 42.51 seconds is closer but still a bit below the calculated approximate time. 60.00 seconds is greater than the 52 second rough upper bound and would imply a speed lower than 1 metre per second. Only 45.61 seconds aligns with the exact calculation using the given rate.

Common Pitfalls:
A typical mistake is to multiply 52 by 1.14 instead of dividing, which reverses the roles of speed and time. Another error is ignoring the units and misinterpreting centimetres for metres or vice versa. Some students also round too early during calculation, which can push them toward an incorrect option. Keeping the formula time = distance / speed clear in mind prevents most of these errors.

Final Answer:
The loom will take approximately 45.61 seconds to weave 52 metres of cloth.