A tank has an inlet tap and a discharge tap. The inlet tap takes 40 minutes to fill the tank while the discharge tap takes one hour to empty the tank. If the tank was empty and the two taps were opened at the same time
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We are given:
Inlet tap fills the tank in 40 minutes fills 1/40 of the tank per minute
Discharge tap empties the tank in 60 minutes empties 1/60 of the tank per minute
Step 1: Find the net filling rate
Let’s calculate the net rate of filling when both taps are open:
Net rate = 1/40 - 1/60
Find LCM of 40 and 60:
LCM(40,60) = 120
1/40 = 3/120
1/60 = 2/120
So:
Net rate = 3/120 - 2/120 = 1/120
This means: The tank fills at a rate of 1/120 per minute
Step 2: How much water is in the tank after 10 minutes?
In 10 minutes, the amount filled is:
10 x 1/120 = 10/120 = 1/12
Step 3: How long to fill half the tank?
We want:
1/120 x t = 1/2
t = 1/2 ÷ 120
t = 1/2 x 120 = 60 minutes
Final Answers:
Fraction of tank after 10 minutes: 1/12
Time for tank to be half full: 60 minutes
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