Question

Two pipes together can fill a water tank is 6 hours and 40 minutes. Find the time each will take to fill the tank if one of the two pipes can fill it in 3 hours less than the other.

Answer 1

This the answer of your question

Answer 2

Answer:

The smaller tap will fill the tank in 15 hours and the larger tap will the tank in 12 hours

Step-by-step explanation:

$\text{Let the smaller tap fill the tank in }\frac{1}{x}\text{ hours}\\\\\text{Let the larger tap fills the tank in }\frac{1}{x-3}\text{ hours}$

Total Time = 6 hours 40 minutes

$\implies\text{Total time = } 6\tfrac{40}{60}\text{ hours}\\\\\implies\text{Total Time = }\frac{20}{3}\text{ hours}$

According to the given condition in the problem :

$\frac{1}{x}+\frac{1}{x-3}=\frac{3}{20}\\\\\implies \frac{2x-3}{x^2-3x}=\frac{3}{20}\\\\\implies 3x^2-49x+60=0\\\\\text{Now, solving the above equation. We get, }\\\\x=15\text{ or }x=\frac{4}{3}\\\\\text{Now, }x=\frac{4}{3}\text{ is rejected because the other tap time will become negative in this case}$

So, x = 15

Hence, The smaller tap will fill the tank in 15 hours and the larger tap will the tank in 12 hours