FILL A TANK OR CONTAINER
PROBLEM
In a filling a container problem, you will usually be given two speeds of filling a large container.
Problem: A fish aquarium can be filled in 8 hours with a hose and 12 hours using buckets carried to the fish tank. How long would it take if you were to use the hose AND buckets to fill the aquarium?
Let the time it would take to fill the fish aquarium using both the hose and buckets be the letter t.
The part the hose would be used to do the work is 1/8. The part the buckets would be used to do the work would be 1/12. Working together, the effort to do the work would be combined to be (1/8 + 1/12).
The equation needed to figure out the total time when BOTH the hose and the buckets are used to fill the aquarium is:
t(1/8 + 1/12) = 1 ¬ The 1 represents ONE job being done together.
The common denominator for 1/8 and 1/12 is the number 24. Rename the fractions inside the parenthesis.
t(3/24 + 2/24) = 1
t(5/24) = 1
Undo the 5/24 by multiplying EACH side of the equation by 24/5.
24 (t) 5_ = (1) 24
5 24 5
t = 24/5 = 4.8 hours.
