Question

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
A. 1/3
B. 1/2
C. 1/4
D. 1
E. 5/6

Answer 1

Answer:D) 1 hr

Step-by-step explanation:

Given

Pump A and B can fill tank in $\frac{6}{5} hr$

Pump A and C can fill tank in $\frac{3}{2} hr$

Pump B and C can fill tank in $2 hr$

Let A be the total hr taken A therefore rate of $A=\frac{1}{A} /hr$

Let B be the total hr taken B therefore rate of $B=\frac{1}{B} /hr$

Let C be the total hr taken C therefore rate of $C=\frac{1}{C} /hr$

$\frac{1}{A}+\frac{1}{B}=\frac{5}{6}$-----1

$\frac{1}{B}+\frac{1}{C}=\frac{1}{2}$-----2

$\frac{1}{A}+\frac{1}{C}=\frac{2}{3}$-----3

Adding 1,2 & 3

$2(\frac{1}{A}+\frac{1}{B}+\frac{1}{C})=\frac{5}{6}+\frac{1}{2}+\frac{2}{3}$

$\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{2}{2}$

$\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=1$

thus time taken by A,B and C combined is 1 hr