Respuesta :
Answer:D) 1 hr
Step-by-step explanation:
Given
Pump A and B can fill tank in [tex]\frac{6}{5} hr[/tex]
Pump A and C can fill tank in [tex]\frac{3}{2} hr[/tex]
Pump B and C can fill tank in [tex]2 hr[/tex]
Let A be the total hr taken A therefore rate of [tex]A=\frac{1}{A} /hr[/tex]
Let B be the total hr taken B therefore rate of [tex]B=\frac{1}{B} /hr[/tex]
Let C be the total hr taken C therefore rate of [tex]C=\frac{1}{C} /hr[/tex]
[tex]\frac{1}{A}+\frac{1}{B}=\frac{5}{6}[/tex]-----1
[tex]\frac{1}{B}+\frac{1}{C}=\frac{1}{2}[/tex]-----2
[tex]\frac{1}{A}+\frac{1}{C}=\frac{2}{3}[/tex]-----3
Adding 1,2 & 3
[tex]2(\frac{1}{A}+\frac{1}{B}+\frac{1}{C})=\frac{5}{6}+\frac{1}{2}+\frac{2}{3}[/tex]
[tex]\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{2}{2}[/tex]
[tex]\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=1[/tex]
thus time taken by A,B and C combined is 1 hr
