two pipes running together can fill a tank in 11 1/9 minutes if one pipe takes 5 minutes more - Math - Quadratic Equations

Question

two pipes running together can fill a tank in 11 1/9 minutes if
one pipe takes 5 minutes more than the other to fill the tank
seperately , find the time taken by each pipe to fill the tank
seperately

Gursheen kaur. · Accepted Answer

Given: Two pipes operating simultaneously can fill a tank in $11 \frac{1}{9} \min u t e s = \frac{100}{9} \min u t e s$ Let one pipe can fill a tank in x minutes Therefore, other pipe will take (x + 5) minutes to fill the tank Work done by both the pipe together in 1 minutes is: $\frac{1}{x} + \frac{1}{x + 5} = \frac{1}{\frac{100}{9}} \Rightarrow \frac{x + 5 + x}{x (x + 5)} = \frac{9}{100} \Rightarrow 200 x + 500 = 9 x^{2} + 45 x \Rightarrow 9 x^{2} - 155 x - 500 = 0 \Rightarrow 9 x^{2} - 180 x + 25 x - 500 = 0 \Rightarrow 9 x (x - 20) + 25 (x - 20) = 0 \Rightarrow (x - 20) (9 x + 25) = 0 \Rightarrow x = 20, \frac{- 25}{9}$ As x can't be negative Therefore, x = 20 minutes Hence, one pipe will take 20 minutes and second pipe will take 20 + 5 = 25 minutes separately to fill the tank

two pipes running together can fill a tank in 11 1/9 minutes. if one pipe takes 5 minutes more than the other to fill the tank seperately , find the time taken by each pipe to fill the tank seperately .