SOLUTION: Suppose that one hose can fill a small pool in 4 hours, and a second hose can fill the pool in 3 hours. a) Write an equation whose solution gives the time needed for the hoses, w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Suppose that one hose can fill a small pool in 4 hours, and a second hose can fill the pool in 3 hours. a) Write an equation whose solution gives the time needed for the hoses, w      Log On


   

Question 919606: Suppose that one hose can fill a small pool in 4 hours, and a second hose can fill the pool in 3 hours.
a) Write an equation whose solution gives the time needed for the hoses, working together, to fill the pool.
b) Solve the equation in part (a)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
You are looking for the sum of the rates of the two hoses, and the unit is POOLS per HOUR.

1%2F4%2B1%2F3, but what you are really asked, is the reciprocal, meaning the TIME to fill 1 pool.

highlight%281%2F%281%2F4%2B1%2F3%29%29 HOURS per POOL.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose that one hose can fill a small pool in 4 hours, and a second hose can fill the pool in 3 hours.
a) Write an equation whose solution gives the time needed for the hoses, working together, to fill the pool.
b) Solve the equation in part (a)

a.
Let time it takes both to fill pool, be T

Slower hose fills pool in 4 hours, or 1%2F4 of pool in 1 hour
Faster hose fills pool in 3 hours, or 1%2F3 of pool in 1 hour
Equation to determine time taken to fill pool, with both hoses working: highlight_green%28highlight_green%281%2F4+%2B+1%2F3+=+1%2FT%29%29
b.
Solve for T.