Q2. A tank with a capacity of 1000 litres could be filled up using Taps A and B. Tap A and Tap B are used at different times to fill up the tank.
(a) If Tap A supplies water to the tank at a rate of x litres per minute, write down an expression for the time taken, in minutes, by Tap alone to fill up the tank completely.
(b) Tap B supplies water to the tank at a rate of 20 litres per minute faster than Tap A. Write down an expression for the time taken, by Tap B alone to fill up the tank completely.
(c) Given that the difference in time by Tap A and Tap B to fill the tank separately is 1 hour, form an expression in terms of x and show that it reduces to 3x^2 + 60x - 1000 = 0.
(d) Solve the equation 3x^2 + 60x - 1000 = 0, giving your answers correct to two decimal places.
(e) if Tap And Tap B are both turned on together to fill the tank when it is empty, find the time taken, correct to the nearest minute, for the tank to be completely filled.