Question

There are 3 taps for three pipes x, y and z. x and y are inlet pipes, which can fill the tank in 20 hours and 25 hours respectively, whereas z is an outlet tap. When the tank is empty, a man want to turn on x and y, but by mistake he turned on x and z. It takes 10 hours more to fill the tank than expected. In how much time can pipe z empty the tank alone

Answer 1

This looks like a simple system of equations problem. Write out formulas and do system of equations to figure out z

Answer 2

1/20+1/25=1/z

Answer 3

1/20+9/100=10

Answer 4

If x and y are turned on, how long will it take to fill the tank?
Use 1/x + 1/y = 1/t . t = xy / (x+y)
If x and z are turned on, how long will it take to fill the tank?
Use 1/x - 1/z = 1/t1 t1 = xz / (z-x)

"It takes 10 hours more to fill the tank than expected."
t1 - t = 10

xz / (z-x) - xy / (x+y) = 10

Put x = 20, y = 25 and solve for z.

Answer 5

z=380