Question

3. Solve the following.
a. If 7 taps can fill a tank in 5 hours, how many hours will 4 taps take to fill the same tak​

Answer 1

Answer:

A tap can fill a tank in 4 hours. Another tap can empty it in 6 hours. How long will it take to fill the tank if both taps are open?

If we assume a sixty litre tank, then the math is easier.

4 hrs of in flow gives us a full 60L. thus the in-flow rate is 15 L/hr

6 hours of out flow to empty a full 60 L, gives us an out flow rate of 10 L/hr.

Both taps are open, 15 in per hour, 10 out per hour, overall flow rate is plus 5L per hour. 60L divided by 5 equals 12 hours.

It will take 12 hours to fill the tank.

To prove that this works for a tank of any size, takes a bit of algebra.

tank size of X litres. 4 hours to fill means a flow rate of 1/4X L/hr. 6 hours to empty means a flow rate of 1/6X L/hr. to find the difference in the flow and thus the remainder in the tank after any given hour, we subtract the flow rates.

1/4X minus 1/6X is the same as 3/12X minus 2/12X which is 1/12X L/hr. thus to get a full tank of X Litres, would require 12 hours.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

7 taps takes time = 5 hours

then,

1 tape will take time = 5/7 hours

then,

4 tapes will take time = 4×5/7 hours

= 20/7 hours

= 2.85 hours

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