P, Q, and R finish a project in 24, 6, and 12 days respectively. Working collectively, the task will be finished in________days.
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Answer: B. 3 3⁄7
Explanation
Individual work rates for p, q, and r are one twenty fourth, one sixth, and one twelfth. Summing these fractions gives a combined work rate of seven twenty fourths per day. Inverting this combined rate yields twenty four sevenths, which simplifies to three and three sevenths days. Combined work rates sum individual unit productivity fractions together. Inverting the sum of work rates calculates total collaborative project duration. Mixed numbers express fractional completion times in accessible everyday units.
Project teams combine member productivity rates to estimate joint task completion times. Manufacturing supervisors calculate assembly line output speeds using worker collaboration data. Contractors schedule multi worker tasks to optimize labor efficiency on sites. Option A underestimates total collaborative days by miscalculating rate sums. Option C overestimates the time required for the collective team to finish. Option D rounds the completion time incorrectly to a whole number of days.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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