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A warehouse can fulfill an order using either of two packing lines. Line 1 alone fulfills the order in 10 hours; Lines 1 and 2 together fulfill it in 6 hours. If Line 2 works alone for 5 hours and then Line 1 joins it, how many additional hours are needed to finish the order?
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Correct answer
C
Line 1 rate = 1/10 per hour. Combined rate = 1/6, so Line 2 rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15 per hour.
In 5 hours alone, Line 2 completes 5/15 = 1/3 of the order, leaving 2/3. Together the lines do 1/6 per hour, so time = (2/3) ÷ (1/6) = (2/3) × 6 = 4 hours.
A common slip lands on 2 by mistaking the 1/3 Line 2 finishes for the work still remaining and dividing that by 1/6; the 1/3 is the part already done, so the remaining 2/3 is what must be divided by the combined rate.
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