Question

water tank has inlets of two types a and b. all inlets of type a when open, bring in water at the same rate. all inlets of type b, when open, bring in water at the same rate. the empty tank is completely filled in 30 minutes if 10 inlets of type a and 45 inlets of type b are open, and in 1 hour if 8 inlets of type a and 18 inlets of type b are open. in how many minutes will the empty tank get completely filled if 7 inlets of type a and 27 inlets of type b are open?

Answer 1

There is no solution for the given conditions of the water tank problem.

Step-by-step explanation:

To solve this problem, we can start by setting up a system of equations. Let x represent the amount of time it takes to fill the tank when 7 inlets of type a and 27 inlets of type b are open. According to the given information, when 10 inlets of type a and 45 inlets of type b are open, the tank is filled in 30 minutes. This can be represented by the equation 10a + 45b = 1/30.

Similarly, when 8 inlets of type a and 18 inlets of type b are open, the tank is filled in 1 hour. This can be represented by the equation 8a + 18b = 1/60.

We now have a system of equations:

10a + 45b = 1/30

8a + 18b = 1/60

To solve this system, we can multiply the second equation by 5 to make the coefficients of 'a' in both equations equal:

40a + 90b = 1/12

40a + 45b = 1/30

Subtracting the second equation from the first, we get 45b - 45b = 1/30 - 1/12, which simplifies to 0 = -1/20.

Since this is not a valid equation, there is no solution for this system. Therefore, there is no value of x that satisfies the given conditions.