Pipe $A$ can fill a tank in $4$ hrs. If pipe $B$ works alone, it takes $3$ hrs longer to fill the tank than if both pipes work together. How long will it take for pipe $B$ to fill the tank if it works alone?
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$5.275$ hrs
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$6.275$ hrs
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$4.275$ hrs
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None of these
A
Correct answer
Explanation
Let A take 4 hrs, B take x hrs. Together they take 4x/(4+x) hrs. Given x = 4x/(4+x) + 3. x = (4x + 12 + 3x)/(4+x). x(4+x) = 7x + 12. x^2 + 4x = 7x + 12. x^2 - 3x - 12 = 0. x = [3 + sqrt(9 - 4*1*-12)] / 2 = [3 + sqrt(57)] / 2 = (3 + 7.55) / 2 = 5.275.