PS : Pumps A,B,C

[Xbond]

Hi there,

Could help me to understand why the right answer of this PS is E. I pick B but I didn't find why it is E
A complete explanation is welcome.

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) 2/3
D) 5/6
E) 1

[Testluv]

Hi there,

Could help me to understand why the right answer of this PS is E. I pick B but I didn't find why it is E
A complete explanation is welcome.

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) 2/3
D) 5/6
E) 1

Rate and time are always inversely related:

AB's rate is 6/5, so in 1 hour, AB will do 5/6 of the job.
AC's rate is 3/2, so in 1 hour, AC will do 2/3 of the job.
BC's rate is 2, so in 1 hour, BC will do 1/2 of the job.

Let the number of units in the total job be a number that is a multiple of 6, 3, and 2; let's say there are 18 units in the total job.

Then, in one hour:

AB will complete 5/6*18 = 15 units;
AC will complete 2/3*18 = 12 units;
BC will complete 1/2*18 = 9 units.

Summing up:
2 As, 2 Bs, and 2Cs complete 36 units.
So, in one hour, 2 of each of the pumps will complete two jobs. Therefore, it will take 1 of each of the pumps 1 hour to complete the job.

[Xbond]

many thks

[batbond007]

Other way

1/Total time = 1/A + 1/B + 1/C + ... + 1/N

1/time for 2A + 2B + 2C = 5/6 + 2/3 + 1/2 = 2 hrs

Hence time for 2A + 2B + 2C = 1/2 hrs

Hence time for A + B + C = 1 hr.