Finishing time from partial completion at a constant rate: A person works on a project and completes 5/8 of the job in 10 days at a steady pace. Assuming the same rate continues, how many more days will he require to finish the remaining work?

Introduction / Context:
Work-completion problems often give a fraction of the job completed over a certain time. We convert this to a daily work rate and then scale to the unfinished fraction to compute the additional days required at the same efficiency.

Given Data / Assumptions:

• Portion completed in 10 days = 5/8 of the job
• Rate is constant over all days
• Goal: time to complete remaining 3/8

Concept / Approach:
Daily work rate r = (completed fraction) / (days). Remaining time = (remaining fraction) / r. This linear model assumes no productivity change and no multitasking effects.

Step-by-Step Solution:
Rate r = (5/8) / 10 = 5 / 80 = 1 / 16 job per dayRemaining fraction = 1 − 5/8 = 3/8Additional days = (3/8) / (1/16) = (3/8) * 16 = 6 days

Verification / Alternative check:
At 1/16 job per day, 6 days completes 6/16 = 3/8, exactly what remains. The arithmetic is fully consistent with the stated rate.

Why Other Options Are Wrong:
8 and 10 overshoot the needed time; 12 doubles the requirement; 7 is close but not exact for the precise rate calculated.

Common Pitfalls:
Incorrectly computing rate as 10 / (5/8), or forgetting to subtract 5/8 from 1 to get the remaining fraction. Keep fractions aligned before multiplying or dividing.

Final Answer:
6