Question

tow taps together can fill a tank completely in 3×1÷13 minutes. the smaller tap taked 3 minutes more than the bigger tap to fill the tank. how much time does each tap take to fill the tank completely ?​

Answer 1

hope it helps

see attachment

Answer 2

Step-by-step explanation:

First pipe takes 5 min to fill and the second pipe takes 8 min to fill the tank.

Solution:

Let us assume that the first pipe will take x min to fill the tank;

So the second pipe will take(x+3)(x+3) min to fill the tank.

Both the pipes take total 3 \frac{1}{3} m i n=\frac{40}{13} m i n3

3

1

min=

13

40

min

So now, First pipe fill the part in 1 min is \frac{1}{x}

x

1

And second pipe fill the part in 1 min is \frac{1}{x+3}

x+3

1

So,

\frac{1}{x}+\frac{1}{x+3}=\frac{13}{40}

x

1

+

x+3

1

=

40

13

\frac{2 x+3}{x^{2}+3 x}=\frac{13}{40}

x

2

+3x

2x+3

=

40

13

80 x+120=13 x^{2}+39 x80x+120=13x

2

+39x

(x-5)(13 x+24)=0(x−5)(13x+24)=0

x=5 \text { or } x=-\left(\frac{24}{13}\right)x=5 or x=−(

13

24

)

As x value cannot be negative,

hence x =5,

First pipe take 5 min to fill and the second pipe take (5+3) = 8 min to fill the tank.

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