SOLUTION: Three taps p,q,r can fill a tank in 8,10 & 12 hours respectively.Tap p is opened at 8am tap q at 10am & tap r at 11am . At what time would the tank be full? A) 12:12 p.m B) 12:42

Algebra ->  Equations -> SOLUTION: Three taps p,q,r can fill a tank in 8,10 & 12 hours respectively.Tap p is opened at 8am tap q at 10am & tap r at 11am . At what time would the tank be full? A) 12:12 p.m B) 12:42      Log On


   

Question 824583: Three taps p,q,r can fill a tank in 8,10 & 12 hours respectively.Tap p is opened at 8am tap q at 10am & tap r at 11am . At what time would the tank be full?
A) 12:12 p.m
B) 12:42 p.m
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Three taps p,q,r can fill a tank in 8,10 & 12 hours respectively.
Tap p is opened at 8am tap q at 10am & tap r at 11am .
At what time would the tank be full?
:
let t = tap p operating time
then
(t-2) = tap q operating time
and
(t-3) = tap r operating time
:
Let the full tank = 1
:
t%2F8 + %28%28t-2%29%29%2F10 + %28%28t-3%29%29%2F12 = 1
multiply 120 to clear the denominators
15t + 12(t-2) + 10(t-3) = 120
15t + 12t - 24 + 10t - 30 = 120
combine like terms
15t + 12t + 10t - 24 - 30 = 120
37t - 54 = 120
37t = 120 + 54
37t = 174
t = 174/37
t = 4.7 hrs which is 4 + .7(60) = 4 hr 42 min
Find the time
8:00 + 4:42 = 12:42 time to be full