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# 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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Word problems on quadratic equation in one variable .

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1. 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,

∴ 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) = x² + 10x

x² -16x-80 = 0

x² -20x+4x-80=0

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

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

If (x-20)= 0    & (x+4) = 0

∴ x= 20        & x = -4

Because time taken can’t be negative,

∴ timextime taken by the pipe with larger diameter (x) =  20 hours

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

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