Question

two water taps A and b together can fill a tank in 12 hours. tap A takes 10 hours less than the time taken by tap B to fill the tank separately. find the time by tap to fill the tank

Answer 1

Answer:

30 hrs

Explanation:

Let the time taken by time by a be x then the time taken by tap b will be

x + 10

The two taps take 12 hours to fill the tank.

In 1 hour the amount filled will be :

1/x + 1/(x + 10) = 1/12

From this we can get the value of x.

12[x+10 + x] = x(x + 10)

24x + 120 = x² + 10x

x² + 10x - 24x - 120 = 0

x² - 14x - 120 = 0

We need to get the roots of the equation:

The roots are - 20 and 6

x² - 20x + 6x - 120 = 0

x(x - 20) +6(x - 20) = 0

(x + 6)(x - 20) = 0

x = - 6 or 20

Since we are dealing with time and time can never be negative we will take the positive value of x.

Tap a alone takes 20 hours to fill the tank while tap b takes 30 hours to fill the tank alone.