**Word problems on quadratic equation in one variable .**

Deepak BoraNewbie

# To fill a swimming pool two pipes are to be used . If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter is used 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 the smaller diameter takes 10 hours more than the pipe of the larger diameter to fill the pool

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Let time taken by the pipe with larger diameter(A) = x hours,

And time taken by the pipe with smaller diameter (B)= (x+10) hours,

âˆ´ A’s one hour work = 1/x

B’s one hour work = 1/(x+10)

Work done by A in 4 hour = 4/x

Work done by B in 9 hours = 9/x+10

According to the question

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

After Taking LCM & cross multiplying

2(13x+40) = xÂ² + 10x

xÂ² -16x-80 = 0

xÂ² -20x+4x-80=0

x(x-20) +4(x-20)= 0

(x-20)(x+4)= 0

If (x-20)= 0Â Â & (x+4) = 0

âˆ´ x= 20Â Â Â Â & x = -4

Because time taken can’t be negative,

âˆ´ timextime taken by the pipe with larger diameter (x) =Â 20 hours

And time taken by the pipe with smaller diameter (x+10) = 30 hours