52. To fill a swimming pool two pipes are used. If the pipe of larger

1.	52. To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours andthe pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find how long itwould take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hoursmore than the pipe of larger diameter to fill the pool.
Answer» Let x hours be the total time taken by the larger pipe to fill the tank so in 1 hour it would fill 1/x part of the tank similarly y hours are needed for the smaller pipe ,then in 1 hour it would fill 1/y part so, y=10+x -(1) 4/x + 9/y = 1/2 using (1),4/x + 9/10+x =1/2 -(2) solve (2), to get x^2 -16x-80=0 (x-20)(x+4)=0since value of x cannot be -vetherefore x=20 and y=30

52. To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours andthe pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find how long itwould take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hoursmore than the pipe of larger diameter to fill the pool.

Answer»

Let x hours be the total time taken by the larger pipe to fill the tank

so in 1 hour it would fill 1/x part of the tank

similarly y hours are needed for the smaller pipe ,then in 1 hour it would fill 1/y part

so, y=10+x -(1)

4/x + 9/y = 1/2

using (1),4/x + 9/10+x =1/2 -(2)

solve (2), to get

x^2 -16x-80=0

(x-20)(x+4)=0since value of x cannot be -vetherefore x=20 and y=30