Tap \(A\) can fill the tank at a speed of \(x\) litres per minute. Write down an expression, in terms of \(x\), for the duration (in minutes) taken by Tap \(A\).[1]
Tap \(B\) can fill the tank at a speed of \((x-2)\) litres per minute. Write down an expression, in terms of \(x\), for the duration (in minutes) taken by Tap \(B\).[1]
Tap \(B\) will take 30 minutes longer than Tap \(A\) to fill the tank. Write down an equation in \(x\) and show that it reduces to \(15x^2-30x-3853=0\).[3]
Solve the equation \(15x^2-30x-3853=0\), leaving your answers to 2 decimal places.[3]
Hence, find the time taken for the tank to be filled if both taps are turned on, correct your answer to the nearest minute.[2]
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Answer:(a) \(\dfrac{3853}{x}\) min (b) \(\dfrac{3853}{x-2}\) min (c) \(\dfrac{3853}{x-2}-\dfrac{3853}{x}=30\) (d) \(-15.06\) or \(17.06\) (e) \(120\) minutes