two taps running together can fill a tank in 6 hours . If one tap takes 5 hours more than the other tap to fill the tank alone. Find the time taken by each tank alone.
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Let time taken by tap 1=x
and time taken by tap 2=y
Tank filled in 1 hr
1/x+1/y=1/6
x=y+5
1/y+5+1/y=1/6
2y+5/y(y+5)=1/6
12y+30=y²+5y
y²-7y-30
y²-10y+3y-30
y(y-10)+3(y-10)
(y-10)(y+3)
y=10
y=-3
Time can't be negative.
y=10 Hrs
x=15 Hrs
and time taken by tap 2=y
Tank filled in 1 hr
1/x+1/y=1/6
x=y+5
1/y+5+1/y=1/6
2y+5/y(y+5)=1/6
12y+30=y²+5y
y²-7y-30
y²-10y+3y-30
y(y-10)+3(y-10)
(y-10)(y+3)
y=10
y=-3
Time can't be negative.
y=10 Hrs
x=15 Hrs
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