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Answer :
The first leak was detected approximately 23.53 days after the initial filling of the tank.
To determine how many days had passed until the first leak was detected, we need to find the time t when the volume V of water in the tank reaches the point where Leak 1 ends and Leak 2 begins.
The equation representing the volume of water in the tank during Leak 1 is V = -850t + 20000. The tank started with 20000 liters of water and was empty when Leak 1 ended, so we set V to 0 and solve for t:
Set the equation to zero: 0 = -850t + 20000
Add 850t to both sides: 850t = 20000
Solve for t: t = 20000 / 850
Calculate t: t ≈ 23.53 days
Therefore, approximately 23.53 days after the initial filling of the tank.
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