An industrial loom weaves 0.128 metres of cloth every second. Approximately how many seconds will it take for the loom to weave 25 metres of cloth at this constant rate?

Introduction / Context:
This problem is another example of using the relationship between distance, speed, and time, which is a core part of chain rule style questions. We are given how many metres of cloth an industrial loom weaves each second, and we must compute the total time required to weave a specified total length. The focus here is careful division and sensible approximation to match a multiple choice option.

Given Data / Assumptions:

• Weaving speed of the loom = 0.128 metres per second.
• Total cloth required = 25 metres.
• The weaving rate is assumed to be constant for the entire duration.
• We need the approximate time in seconds, selecting from the provided options.

Concept / Approach:
Using the standard formula, time = distance / speed we substitute the total distance in metres and the speed in metres per second to get time in seconds. Because the numbers are fractional, we expect a non integer result, which we then approximate to the closest option given. This is a straightforward numerical calculation with a clear proportional meaning.

Step-by-Step Solution:
Speed of loom = 0.128 metres per second Required distance = 25 metres time in seconds = 25 / 0.128 Compute the division: 25 / 0.128 ≈ 195.31 seconds This is slightly above 195 and below 196, so the closest integer is 195 seconds Therefore, the approximate time required is 195 seconds

Verification / Alternative check:
As a quick check, multiply 0.128 by 200 seconds and see the distance. 0.128 * 200 = 25.6 metres So in 200 seconds the loom weaves about 25.6 metres, which is a bit more than 25 metres. Therefore, in slightly less than 200 seconds it should weave exactly 25 metres. The value 195 seconds fits this reasoning nicely, since 195 is a little less than 200 and 25.6 metres is just a little more than 25 metres.

Why Other Options Are Wrong:
194 seconds gives a smaller distance than 25 metres because it is slightly too short compared to our precise calculation. 196 seconds and 197 seconds are both larger than the calculated 195.31 seconds and therefore represent slightly longer times than needed. 205 seconds is significantly larger and would overshoot the required distance by a wider margin. Among all options, 195 seconds is the closest to the exact computed value.

Common Pitfalls:
A frequent error is inverting the formula and computing 25 * 0.128 instead of 25 / 0.128, which would incorrectly reduce the time instead of increasing it. Some learners also misread 0.128 as 0.0128 or 1.28, leading to large errors. Rounding too early in the computation, for example using 0.13 instead of 0.128, can also shift the final answer away from the correct choice. Careful handling of decimals and clear use of the time formula are essential.

Final Answer:
The loom will take approximately 195 seconds to weave 25 metres of cloth.