SOLUTION: A tank can be filled using hose A alone in 3 hours, using hoses A and B together in 72 minutes, and using hoses A, B and C together in 40 minutes. How many minutes will it take to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tank can be filled using hose A alone in 3 hours, using hoses A and B together in 72 minutes, and using hoses A, B and C together in 40 minutes. How many minutes will it take to       Log On


   

Question 573666: A tank can be filled using hose A alone in 3 hours, using hoses A and B together in 72 minutes, and using hoses A, B and C together in 40 minutes. How many minutes will it take to fill the same tank using only hose C?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A tank can be filled using hose A alone in 3 hours, using hoses A and B together in 72 minutes, and using hoses A, B and C together in 40 minutes.
How many minutes will it take to fill the same tank using only hose C?
:
Find how long for B to fill it alone
Let a full tank = 1
Convert 3 hrs to 180 min
:
72%2F180 + 72%2FB = 1
multiply by 180B, results
72B + 180(72) = 180B
12960 = 180B - 72B
12960 = 108B
B = 12960%2F108
B = 120 minutes, B alone
:
Find C
40%2F180 + 40%2F120 + 40%2FC = 1
multiply by 360C, results:
2C(40) + 3C(40) + 360(40) = 360C
80C + 120C + 14400 = 360C
14400 = 360C - 200C
14400 = 160C
C = 14400%2F160
C = 90 minutes for C alone
:
:
Check that using decimals
40%2F180 + 40%2F120 + 40%2F90 =
.22 + .33 + .44 = .99 ~ 1 a full tank