SOLUTION: Three pipes, A, B, and C are often used two at a time to fill a tank. When A and B are used together, the tank is filled in 5 minutes. When either A and C or B and C are used toget

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Three pipes, A, B, and C are often used two at a time to fill a tank. When A and B are used together, the tank is filled in 5 minutes. When either A and C or B and C are used toget      Log On


   

Question 415603: Three pipes, A, B, and C are often used two at a time to fill a tank. When A and B are used together, the tank is filled in 5 minutes. When either A and C or B and C are used together, the tank is filled in 3 minutes. How long would it take each pipe alone to fill the tank?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Three pipes, A, B, and C are often used two at a time to fill a tank.
When A and B are used together, the tank is filled in 5 minutes.
When either A and C or B and C are used together, the tank is filled in 3 minutes.
How long would it take each pipe alone to fill the tank?
:
Let the full tank = 1
5%2Fa + 5%2Fb = 1
and
3%2Fa + 3%2Fc = 1
or
3%2Fb + 3%2Fc = 1
:
Use elimination with the 2nd and 3rd equations:
3%2Fa + 3%2Fc = 1
3%2Fb + 3%2Fc = 1
-----------------------------Subtraction eliminates 3/c
3%2Fa - 3%2Fb = 0
therefore
3%2Fa = 3%2Fb
therefore
a = b
:
using the 1st equation, replace b with a
5%2Fa + 5%2Fa = 1
10%2Fa = 1
a = 10 hrs alone
then
b = 10 hrs alone
:
Find c:
3%2F10 + 3%2Fc = 1
Multiply by 10c
3c + 10(3) = 10c
30 = 10c - 3c
30 = 7c
c = 30%2F7
c = 42%2F7 hrs alone
:
Summarize: A = 10 hrs, B = 10 hrs, C = 42%2F7 hrs
:
:
You can check this in the original equations using; C=4.2857