SOLUTION: A tank can be filled by a certain pipe in 18 hours. Five hours after this pipe is opened, it is supplemented by a smaller pipe which, by itself, could fill the tank in 24 hours. Fi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tank can be filled by a certain pipe in 18 hours. Five hours after this pipe is opened, it is supplemented by a smaller pipe which, by itself, could fill the tank in 24 hours. Fi      Log On


   

Question 910643: A tank can be filled by a certain pipe in 18 hours. Five hours after this pipe is opened, it is supplemented by a smaller pipe which, by itself, could fill the tank in 24 hours. Find the total time, measured from the opening of the larger pipe, to fill the tank.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Main objective first, is to derive an equation which represents the situation. The final objective is to solve the equation.


RATES AS TANK per HOUR
Certain Pipe, 1%2F18
Smaller Pipe, 1%2F24
Certain Plus Smaller, 1%2F18%2B1%2F24

Simplify the combined pipes rate.
1%2F18%2B1%2F24
1%2F%283%2A2%2A3%29%2B1%2F%282%2A2%2A2%2A3%29, LCD is 2*2*2*3*3=72
%281%2F18%29%284%2F4%29%2B%281%2F24%29%283%2F3%29
4%2F72%2B3%2F72
highlight_green%287%2F72%29-----the pipes combined rate working together

The situation:
Certain pipe operates for 5 hours, and then the smaller pipe is also opened; and for an unknown amount of additional time, the tank is full. Let t be this additional time, which later we want to ADD to 5.

EQUATION:
highlight%28%281%2F18%29%2A5%2B%287%2F72%29%2At=1%29.
Solve for t, and add to find highlight%28t%2B5%29.