Question

5. A tank fills completely in 2 hours if both the taps are open. If
only one of the taps is open at the given time, the smaller tap
takes 3 hours more than the larger one to fill the tank. How much
time does each tap take to fill the tank completely ?

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Answer 1

Step-by-step explanation:

let, large tap takes x hours

let, large tap takes x hours smaller tap takes x+3 hrs

let, large tap takes x hours smaller tap takes x+3 hrsif both taps are opened tank fills in 2hrs

let, large tap takes x hours smaller tap takes x+3 hrsif both taps are opened tank fills in 2hrsAmount of water filled in 1 hr by large tap is 1/x.

Amount of water filled in 1 hr by small tap is 1/(x+3).

Amount of water filled in 2hrs is 1/2.

1/x +1/(x+3) = 1/2

2x+3/(x^2 +3x) = 1/2

4x + 6 = x^2+3x

x^2 - x - 6 = 0

x^3 - 3x + 2x - 6 = 0

(x - 3) (x + 2) = 0

x = 3, -2

Amount of water filled in 3hr by large tap alone.

Amount of water filled in 6 hr by small tap alone.

Answer 2

Answer:

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