Question : To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is 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.
Doubt by Sarthak
Solution :
Let the time taken by the pipe of larger diameter = x hours
Fraction of tank filled by pipe of larger diameter in 1 hour = 1/x
Fraction of tank filled by pipe of larger diameter in 4 hours = 4/x
Fraction of tank filled by pipe of smaller diameter in 1 hour = 1/(x+10)
Fraction of tank filled by pipe of larger diameter in 9 hours = 9/(x+10)
ATQ
x²-20x+4x-80=0
x(x-20)+4(x-20)=0
(x+4)(x-20)=0
x+4 = 0
x = -4
Hence, time taken by the pipe of larger diameter
= x hours
= 20 hours
and the time taken by the pipe of smaller diameter
= (x+10) hours
= (20+10) hours