It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is uses for 9 hours, only half the pool can be filled. How long would it take each pipe to fill the pool seperately? Please give proper solution!
Answers
let the time taken by the first pipe be x hours and the time taken by the second pipe be y hours.
in 1 hour the first pipe can fill it = 1/x
in 1 hour the second pipe can fill it = 1/y
1/x +1/y = 1/12 --------------(1)
4/x = 9/9 =1/2---------------(2)
Consider 1/x be a and 1/y be b.
a + b = 1/12 -------------(3)
4a + 9b = 1/2 ----------------(4)
multiply 3 by equ (4) and then subtract equ(5) from equ(4).
4a + 4b =1/3 --------------(5)
we get, b = 1/30
y = 30.
sustituting the value of y in equ(3) we get
a + 1/30 = 1/12
x = 20.
Hence the first pipe would take 20hours and the second pipe would take 30 hours.
let the time taken by the first pipe be x hours and the time taken by the second pipe be y hours.
in 1 hour the first pipe can fill it = 1/x
in 1 hour the second pipe can fill it = 1/y
1/x +1/y = 1/12 --------------(1)
4/x = 9/9 =1/2---------------(2)
Consider 1/x be a and 1/y be b.
a + b = 1/12 -------------(3)
4a + 9b = 1/2 ----------------(4)
multiply 3 by eq. (4) and then subtract eq.(5) from eq.(4).
4a + 4b =1/3 --------------(5)
we get, b = 1/30
y = 30.
substituting the value of y in eq. (3) we get
a + 1/30 = 1/12
x = 20.
Hence the first pipe would take 20hours and the second pipe would take 30 hours.