Answer:
70 minutes
Step-by-step explanation:
Given: One hose can fill a pond in 28 minutes.
2nd hose can fill the same pond in 20 minutes.
One hose can fill [tex]\frac{1}{28}[/tex] of pond per minutes
Both one hose and 2nd hose can fill [tex]\frac{1}{20}[/tex] of pond per minutes.
Lets assume time taken by 2nd hose alone to fill pond be "x".
∴ 2nd hose alone can fill [tex]\frac{1}{x}[/tex] of pond per minute.
Now, forming an equation to show pond filled per minuted by both hoses.
[tex]\frac{1}{28} +\frac{1}{x} = \frac{1}{20}[/tex]
taking LCD as 28x
⇒ [tex]\frac{x+28}{28x} = \frac{1}{20}[/tex]
multiplying both side by 20
⇒ [tex]\frac{20(x+28)}{28x} = 1[/tex]
Using distributive property of multiplication
⇒ [tex]\frac{20x+560}{28x} = 1[/tex]
multiplying 28x on both side.
⇒ [tex]20x+560= 28x[/tex]
subtracting 20x on both side
⇒ [tex]560= 8x[/tex]
dividing both side by 8
⇒[tex]x= \frac{560}{8}[/tex]
∴ x= 70 minutes
Hence, second hose can alone fill the pond in 70 minutes.
