Respuesta :
Answer:
The time taken by smaller pipe to fill the tank alone is 74.2 min
Step-by-step explanation:
Given as :
The time taken by two pipes to fill tank = 19 min
Let the time taken by larger pipe to fill tank = y
And the time taken by smaller pipe to fill tank = x
According to question
The smaller pipe takes 49 minutes longer than larger pipe
I.e x = y + 49
Now,
[tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]
Or, [tex]\dfrac{1}{y + 49}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]
Or, [tex]\dfrac{y + 49 + y}{y^{2} + 49 y }[/tex] = [tex]\dfrac{1}{49}[/tex]
Or, 2 y + 49 = [tex]\dfrac{y^{2}+49y }{19}[/tex]
Or, 19 × ( 2 y + 49 ) = y² + 49 y
Or, 38 y + 931 = y² + 49 y
Or, y² + 49 y - 38 y - 931 = 0
or, y² + 11 y - 931 = 0
Or, Applying quadratic equation method to calculate the value of y
so, y = [tex]\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, y = [tex]\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}[/tex]
Or, y = [tex]\frac{- 1 \pm \sqrt{121+3724}}{2}[/tex]
or, y = [tex]\frac{- 1 \pm \sqrt{3845}}{2}[/tex]
or, y = [tex]\frac{- 1 \pm 62.008}{2}[/tex]
∴ y = 25.2 , - 36.5
So, The time taken by larger pipe = y = 25.2 min
and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min
Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer
