Question
A, B, and C can fill a tank in 12, 15, and 20 minutes respectively. A starts alone; after 3 minutes B joins; after another 2 minutes C joins. How long will they take to fill the tank?
Solution
ATQ,
Work per min: A=1/12, B=1/15, C=1/20 3 min → A: 3/12 = 1/4 Next 2 min → A+B: 2×(1/12+1/15)=2×(9/60)=3/10 Total = 1/4 + 3/10 = 5/20 + 6/20 = 11/20 Remaining = 9/20 All three → per min = (1/12+1/15+1/20)= (5+4+3)/60 = 12/60=1/5 Time = (9/20)/(1/5)= (9/20)*5=9/4=2.25 min Total = 3+2+2.25 = 7.25 minutes.
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