Question

A pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours ,only have the pool can be filled .find how long it to take for each pipe to fill the pool separately .if the pipe of smaller diameter takes 10 hours more than the pipe of diameter to fill the pool

Answer 1

ANSWER:-
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Let the pipe of larger diameter fills the tank in x hrs
In 1hr =1/x
Pipe of smaller diamter fills the tank in x+10hrs

4/x+9/x+10=1/2

4(x+10)+9x/x(x+10)=1/2

4x+40+9x/x^2+10x=1/2 (x^2=square of x)

x^2+10x=80+26x

x^2-16x-80=0
a=1 b=-16 c=-80
b^2-4ac= (-16)^2-4(1)(-80)
= 256+320
= 576=24
Solving by quadratic formula,we get
x=-(-16)+24/2 x=-(-16)-24
x=40/2 x=-8/2
x=20 x=-4

Hence,larger diamtere takes 20 hrs and smaller diameter takes x+10=20+10=30 hrs to fill the tank.