Answer:
90 minutes or 1 hour 30 minutes
Step-by-step explanation:
Time taken to fill t is inversely proportional to number of pipes. We can express this as t ∝ [tex]\frac{1}{n}[/tex] where n is the number of pipes
We can also write this as t = [tex]\frac{k}{n}[/tex] where k is a constant
Using the data given 80 = [tex]\frac{k}{8}[/tex] (1)
For 6 pipes, if the time taken is T then
[tex]T = \frac{k}{6}[/tex] (2)
Dividing (2) by (1) gives
[tex]\frac{T}{80} = \frac{k}{6}[/tex] ÷ [tex]\frac{k}{8}[/tex]
[tex]\frac{k}{6}[/tex] ÷ [tex]\frac{k}{8} = \frac{k}{6} \frac{8}{k} = \frac{8}{6}\\\\[/tex]
So
[tex]\frac{T}{80} = \frac{8}{6}\\\\[/tex]
T = [tex]80 \frac{8}{6}[/tex] (multiplying both sides by 80
And this computes to 90 minutes or 1 hour 30 minutes
