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

Introduction:
This question involves a direct application of the time = distance / speed formula, where the distance is the length of cloth to be woven and the speed is the weaving rate of the industrial loom. It checks your familiarity with rate, time, and distance type problems in a slightly different context of cloth weaving.

Given Data / Assumptions:
Weaving speed of the loom = 0.128 metres per second. Required cloth length = 25 metres. The loom is assumed to operate steadily at this constant rate. We are asked for the approximate time in seconds.

Concept / Approach:
The fundamental relation between distance, speed, and time is: time = distance / speed. Here distance is measured in metres, speed in metres per second, so time will naturally be in seconds. We substitute the given numerical values and then round the result to the nearest whole second to match the options.

Step-by-Step Solution:
Step 1: Write down the formula. time = distance / speed. Step 2: Substitute distance and speed. time = 25 / 0.128 seconds. Step 3: Perform the division. 25 / 0.128 = 195.3125 seconds. Step 4: Round to the nearest whole number. 195.3125 seconds is approximately 195 seconds. Therefore, the loom takes about 195 seconds to weave 25 metres of cloth.

Verification / Alternative check:
We can reverse check by multiplying the approximate time back by the speed: 0.128 * 195 = 24.96 metres (approximately). This is extremely close to 25 metres, and the small difference is due to rounding. If we use the exact time 195.3125 seconds, the cloth length becomes exactly 25 metres. This confirms that 195 seconds is a good approximation.

Why Other Options Are Wrong:
194 seconds corresponds to 0.128 * 194 ≈ 24.83 metres, which is slightly short of the required 25 metres. 196 seconds gives 0.128 * 196 ≈ 25.09 metres, which is slightly more than needed. 197 seconds is even further away at roughly 25.22 metres. 190 seconds would produce only about 24.32 metres, clearly insufficient. The closest and most reasonable approximation among the options is 195 seconds.

Common Pitfalls:
A common mistake is to invert the formula and compute speed / distance instead of distance / speed. Another issue is mishandling decimal division by 0.128, which can lead to calculation errors. Breaking the division into smaller steps or using long division carefully reduces such errors. Also, rounding too early in the computation can cause inaccuracies; always round only at the end when you have the exact numerical result.

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