Answer:
The correct option is C.
Step-by-step explanation:
It is given that at noon the pool was 1/3 full and [tex]1\frac{1}{4}[/tex] hours later it was 3/4 full.
Total parts of pool filled in [tex]1\frac{1}{4}[/tex] hours is
[tex]\frac{3}{4}-\frac{1}{3}=\frac{9-4}{12}=\frac{5}{12}[/tex]
The time can be written as
[tex]1\frac{1}{4}=\frac{5}{4}[/tex]
It means [tex]\frac{5}{12}th[/tex] part of the pool is filled in [tex]\frac{5}{4}[/tex] hours.
Let the pool is filled completely in x hours. So [tex]\frac{5}{12}th[/tex] part of the pool is filled is [tex]\frac{5x}{12}[/tex].
[tex]\frac{5x}{12}=\frac{5}{4}[/tex]
Multiply both sides by 12.
[tex]5x=15[/tex]
Divide both sides by 5.
[tex]x=3[/tex]
The pool is completely filled in 3 hours. Therefore the correct option is C.
