A concrete crew can place 45 cubic yards per day with a 6-person crew. If 180 cubic yards of concrete need to be placed and the schedule allows 3 days, what is the minimum crew size required?
Correct Answer
B) 8 people
Current rate: 45 CY/day ÷ 6 people = 7.5 CY per person per day. Required rate: 180 CY ÷ 3 days = 60 CY/day. Required crew: 60 CY/day ÷ 7.5 CY per person = 8 people.
Why This Is the Correct Answer
Step 1 — Calculate productivity per worker per day: 45 CY/day ÷ 6 workers = 7.5 CY per worker per day. Step 2 — Calculate the required daily output: 180 CY total ÷ 3 days = 60 CY/day needed. Step 3 — Calculate the required crew size: 60 CY/day ÷ 7.5 CY per worker per day = 8 workers. A crew of 8 achieves exactly 60 CY/day, completing the 180 CY in exactly 3 days.
Why the Other Options Are Wrong
Option A: 6 people
6 people is the current crew size, which produces 45 CY/day. At that rate, 180 CY would take 4 days (180 ÷ 45 = 4), one day over the 3-day schedule. Keeping the same crew size does not solve the scheduling constraint.
Option C: 12 people
12 people would produce 12 × 7.5 = 90 CY/day, completing 180 CY in just 2 days — faster than needed but at unnecessary labor cost. The question asks for the minimum crew size to meet the schedule, which is 8, not the maximum possible crew. 12 people is an over-staffed solution.
Option D: 18 people
18 people would produce 18 × 7.5 = 135 CY/day, completing the job in under 2 days — far more crew than needed. This wastes labor resources and significantly increases project cost. The minimum crew needed to meet the 3-day schedule is 8.
Memory Technique
Use the three-step productivity formula: (1) Unit Rate = Total Output ÷ Crew Size, (2) Required Rate = Total Work ÷ Available Days, (3) Required Crew = Required Rate ÷ Unit Rate. Always find the per-person rate first before solving for crew size.
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