Question

two tap together fill a tank in 9 hours 36 minutes the tap of larger diameter takes 8 hours less than the smaller tap to fill tank find time in which each step fill the tank.

Do it hurry please..

Answer 1

hey!!find this solution.........

Answer 2

Answer: The number of hours taken by smaller tap and larger tap are 24 hours and 16 hours respectively.

Step-by-step explanation:

Since we have given that

Number of hours two tap together takes = 9 hours 36 minutes

which can be written as $9\frac{36}{60}=9\frac{3}{5}=\frac{48}{5}\ hours$

Let the number of hours is taken by the smaller tap be x hours.

Let the number of hours is taken by the larger tap be x-8 hours.

According to question,  

$\frac{1}{x}+\frac{1}{x-8}=\frac{5}{48}\\\\\frac{x-8+x}{x(x-8)}=\frac{5}{48}\\\\\frac{2x-8}{x^2-8x}=\frac{5}{48}\\\\\frac{2(x-4)}{x^2-8x}=\frac{5}{48}\\\\48\times 2(x-4)=5(x^2-8x)\\\\5x^2-136x+384=0$

By using quadratic equation, we have,

$x=\frac{16}{5},x=24\\\\\text{ Fraction number will be discarded}\\\\x=24,$

Hence, the number of hours taken by the smaller tap is 24 hours,and the number of hours taken by the larger tap is 24-8=16 hours.