1.Two pipes, A and B, can fill a tank in 12 minutes and 15 minutes respectively. Both pipes are opened simultaneously, but pipe A is closed after 3 minutes. How much additional time will pipe B require to fill the tank completely?
2.Two pipes, A and B, can fill a tank individually in 4 hours and 5 hours respectively. If they are operated alternately for one hour each, how long will it take to fill the tank completely?
3.A tap can fill a tank in 3.5 hours. However, due to a leak at the bottom, it takes an additional 30 minutes to fill the tank completely. How long will the leak take to empty the full tank on its own?
4.Two taps can fill a tank individually in 10 minutes and 15 minutes respectively. When a waste pipe is also open, the tank fills completely in 18 minutes. How long does the waste pipe take to empty the full tank on its own?
5.A tank has a leak that can drain it completely in 20 minutes. When a tap supplying water at 4 liters per minute is opened, the tank takes 24 minutes to empty. What is the total capacity of the tank in liters?
6.Two pipes, P and Q, can fill a tank in 12 minutes and 15 minutes respectively. Both pipes are opened simultaneously, but after 3 minutes, pipe P is closed. How much additional time will pipe Q need to fill the tank completely?
7.Two pipes, A and B, can fill a tank individually in 2 minutes and 15 minutes respectively. If both pipes are opened simultaneously but pipe A is closed after 4 minutes, how long will it take to completely fill the tank?
8.Pipes A and B can fill a tank in 20 minutes and 30 minutes respectively, while pipe C can drain the tank in 40 minutes. If all three pipes are opened simultaneously, how long will it take to fill the tank?
9.What are the solutions to the quadratic equation 3x² - 7x - 6 = 0?
10.What are the solutions to the quadratic equation x² + x - 42 = 0?
11.What are the solutions of the quadratic equation 2x² + 5x + 2 = 0?
12.Given the quadratic equations I. a² - 13a + 42 = 0 and II. b² - 15b + 56 = 0, determine the correct relationship between the values of a and b obtained by solving these equations.
13.Given the equations: (i) a³ − 988 = 343 and (ii) b² − 72 = 49, determine the correct relationship between the values of a and b.
14.Given the quadratic equations I. 9a² + 18a + 5 = 0 and II. 2b² + 13b + 20 = 0, determine the correct relationship between the values of a and b after solving both equations.
15.Given the quadratic equations I. x² + 11x + 30 = 0 and II. y² + 15y + 56 = 0, what is the correct relationship between the values of x and y after solving both equations?
16.Given the quadratic equations I. x² + 3x - 18 = 0 and II. y² + y - 30 = 0, what can be concluded about the relationship between x and y after solving both?
17.Given the equations I. x² + 9x + 20 = 0 and II. y² + 5y + 6 = 0, determine the relationship between the values of x and y after solving both equations.
18.Given the equations I. x² - x - 42 = 0 and II. y² - 17y + 72 = 0, determine the relationship between the values of x and y obtained by solving both equations.
19.Given the equations I. x² + 5x + 6 = 0 and II. y² + 9y + 14 = 0, what can be concluded about the relationship between the values of x and y?
20.Given the equations I. a² + 8a + 16 = 0 and II. b² - 4b + 3 = 0, determine the correct relationship between the values of a and b.