Question

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Question:

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool? Please give me the complete step to do this question....

Answer 1

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)=0

since value of x cannot be -ve
therefore x=20 and y=30