Answered

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two pipes can empty a pool in 3 1/2 hours. if the smaller pipe can empty it in 14 hours alone, how long can the larger pipe empty the same pool alone?

Sagot :

Kaizoku00idn
let P the number of pool to be empty,S is speed,T is time   
P = S x T
smaller pipe 's speed is S
P=1, T =14
1 = S (14)
S = 1/14 pool per hour
bigger pipe's speed is S
let x the time of the bigger pipe to empty a pool , P=1
1= S x
S = 1/x pool per hour

together speed is (1/14) + (1/x) = (x/14x) + (14/14x) = (x+14)/14x pool per hour

back to the formula P = S x T
where P = 1 , T = 7/2 (together time 3 1/2 hour)
1 = [(x+14)/14x] (7/2)
manipulate the equation,
1 = (7x +98)/28x
28x = 7x + 98
28x -7x = 98
21x = 98
x = 98/21
x = 14/3 or 4 2/3
it takes 4 2/3 Hours to empty the pool by the bigger pipe  alone