Question

Two pipes running together can fill a cistern in 3¹/13 minutes if one pipe takes 3 minutes more than the other to fill it. find the time in which each pipe would fill the cistern.

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Answer 1

$\huge\mahfrak{Hello\:Mate}$

$\color{Red}{QUESTION}$

1) Two pipes running together can fill a cistern in 3¹/13 minutes if one pipe takes 3 minutes more than the other to fill it. find the time in which each pipe would fill the cistern.

$\color{Purple}{ANSWER}$

Let faster pipe takes x min to fill the cistern.

To fill the cistern slower pipe take (x+3)

min.

In one minute the faster pipe filled the cistern= 1/x

In 3 1/13= 40/13 min the faster pipe filled the cistern= 40/13 (1/x) = 40/13x

In 3 1/13= 40/13 min the slower pipe filled the cistern= 40/13 (1/x+3) = 40/13(x+3).

ATQ

40/13x + 40/13(x+3) = 1

40/13 [ 1/x + 1/(x+3)] = 1

40 [(x +3+x) / x(x+3)] =13

40(2x +3) =13 x(x+3)]

80x + 120 = 13x +39 x

13 x +39 x -80x -120= 0

13x - 41x -120= 0

13x2 - 65x +24x -120= 0

13x(x -5) + 24(x-5)= 0

(13x +24)(x-5)= 0

(13x +24)= 0 or (x-5)= 0

X =- 24/13 or x = 5

Time cannot be negative, so x = 5

Hence, Faster pipe takes 5 min to fill the cistern while slower pipe takes (x+3) = 5+3= 8 min to fill the cistern.

HOPE THIS WILL HELP YOU...

Answer 2

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