Direct and inverse proportions

Question

Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe is in use when both taps are turned on?

Answer 1

Hi Jerry...

Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe is in use when both taps are turned on?

Given:

A = 6 min to fill tank

B = 9 min to fill tank

C = 15 min to empty tank

Let V=Volume of the tank

Fill Rate x Time = Volume Empty Rate x Time = Volume

Ra x 6min = V Ra = V/6min

Rb x 9 min = V Rb = V/9 min

Rc x 15 min = V Rc = V/15min

Find: The question to answer is when the tank is being filled and emptied through use, how much time will it take to Fill up.

Things to understand:

The volume is the same for all 3 equations above.

The time taken to fill the tank will be the same.

Using Fill Rate x time = Volume

A and B are filling up the tank, C is emptying it

So you will add A and B and subtract C

Ra x t + Rb x t - Rc x t = V

t x (Ra + Rb - Rc) = V

t x (V/6min + V/9min - V/15min) = V

t V x (1/6min + 1/9min - 1/15min) = V

t= 1/ (1/6 + 1/9 - 1/15)

t = 4.74 min

Hope this helps!

Let me know if you have more questions :)