Help solving a work problem..should be easy?

[gen3hatch]

Pumps A, B, C operate at their respective costant rates. Pump A & B operating simultaneously can fll a certain tank in 6/5 hour; pumps A &C can fill a tank simultaneously in 3/2 hour and pump B & C operating simultaneously can fill a tank in 2 hours. How many hours does it take pump A, B, & C operting simultaneously to fill the tank?
A 1/3
B 1/2
C 2/3
D 5/6
E 1

Can you show the work and calculations behind the answer?

[ershovici]

From the question we have three different equotions:
1/A+1/B=6/5 - A+B=5/6
1/A+1/C=3/2 - A+C=2/3
1/B+1/C=2 - B+C=1/2

Add this equptions: 2A+2B+2C=12/6 = 2
2(A+B+C)=2
A+B+C = 1

I THINK ANSWER IS E

[gen3hatch]

Yes. your right..Thanks!

[heshamelaziry]

From the question we have three different equotions:
1/A+1/B=6/5 - A+B=5/6
1/A+1/C=3/2 - A+C=2/3
1/B+1/C=2 - B+C=1/2

Add this equptions: 2A+2B+2C=12/6 = 2
2(A+B+C)=2
A+B+C = 1

I THINK ANSWER IS E

When the questionn says A and B can do a job in 6/5 doesn't it mean that to get to 6/5 we did ------> 1/a + 1/b = 5/6 so A + B = 6/5 ?

I am confused we usually do 1/A + 1/B = 5/6 and then take the reciprocal of 5/6 to get the total time taken by A and B to do one job , so it should be A + B = 6/5


Please help

[aspirant1]

consider work = time x rate
for A+B , time 6/5 hrs

rate A+B = Work/ time; 1/(6/5) = 5/6