Answer:
It will take 18 minutes to fill the trough using both pumps.
Step-by-step explanation:
Given that:
Time taken by pump A = half hour = 30 minutes
Time taken by pump B = three quarters of an hour
One quarter = [tex]\frac{1}{4}[/tex]
One hour = 60 minutes
Three quarters of an hour = [tex]\frac{3}{4}*60[/tex] = 45 minutes
Let,
x be the time taken by both pumps to fill the trough.
[tex]\frac{1}{time\ taken\ by\ pump\ A}+\frac{1}{time\ taken\ by\ pump\ B}=\frac{1}{Time\ taken\ by\ both\ pumps}[/tex]
[tex]\frac{1}{30}+\frac{1}{45}=\frac{1}{x}\\\\\frac{3+2}{90}=\frac{1}{x}\\\\\frac{5}{90}=\frac{1}{x}\\\\\frac{1}{18}=\frac{1}{x}\\x=18[/tex]
Hence,
It will take 18 minutes to fill the trough using both pumps.
