Two pipes running together can fill a tank in \(11\frac{1}{9}\) minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each p ipe would fill the tank separately.
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Two pipes running together can fill a tank in \(11\frac{1}{9}\) minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each p ipe would fill the tank separately.
Two pipes running together can fill a tank in \(11\frac{1}{9}\) minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each p ipe would fill the tank separately.
Let the faster pipe fill the tank in ‘a’ min
Slower pipe fills it in ‘a + 5’ min.
Given, the pipes running together can fill a tank in \(11\frac{1}{9}\) = 100/9 minutes.
In 1 min, part of tank filled = 9/100
\(\Rightarrow \frac{1}{a}+\frac{1}{a\,+\,5}=\frac{9}{100}\)
⇒ 100(a + a + 5) = 9(a2 + 5a)
⇒ 200a + 500 = 9a2 + 45a
⇒ 9a2 – 155a – 500 = 0
⇒ 9a2 – 180a + 25a – 500 = 0
⇒ 9a(a – 20) + 25(a – 20) = 0
⇒ (9a + 25)(a – 20) = 0
⇒ a = 20 mins
Slower pipe will fill it in 25 min