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
Share
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