Portion of work remaining after partial progress: Mohan can mow his entire lawn in x hours at a constant rate. After he works for 2 hours, it begins to rain and he stops. What fraction of the lawn remains unmowed at that moment?

Introduction / Context:
This is a straightforward fraction-of-work problem. If a job takes x hours at a steady rate, then each hour completes an equal fraction of the job. After a certain number of hours, we can compute the completed fraction and subtract from 1 to find what remains.

Given Data / Assumptions:

• Total time to mow entire lawn = x hours.
• Work rate is constant over time.
• Mohan works for 2 hours before stopping.

Concept / Approach:
The fraction of the job completed in t hours at constant speed is t/x. Therefore, the remaining fraction is 1 − t/x. Substitute t = 2 to get the specific fraction left unmowed.

Step-by-Step Solution:
Completed fraction after 2 hours = 2/xRemaining fraction = 1 − 2/x = (x − 2)/x

Verification / Alternative check:
Edge cases: If x = 2 hours (he needs exactly 2 hours to mow all), then remaining = (2−2)/2 = 0, meaning nothing remains—correct. If x is very large, the remaining is close to 1, which is sensible because only a tiny fraction would be done in 2 hours.

Why Other Options Are Wrong:

• 2/x: this is the completed fraction, not the remaining part.
• (2 − x)/2 and x/2: both have wrong structure and units for a fraction of the whole and do not simplify to a value between 0 and 1 for all x > 2.

Common Pitfalls:

• Confusing completed fraction with remaining fraction.
• Not expressing both parts over the common denominator x.

Final Answer:
(x - 2)/x