Math, asked by mehrajdin8473, 1 year ago

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 ? Solve the word problem

Answers

Answered by sijasubbiah
4
Hey

Here is your answer,

Let the volume of the tank be V

Together two taps take 2 hours to fill it completely.

Rate of both the taps together = V/2

Let the two taps be A and B.

Time taken by tap A = t hours

So, rate = V/t

Time taken by tap B = (t + 3) hours

So, rate = V/(t + 3)

Combined rate = V/t + V/(t + 3)

We already know that combined rate = V/2

⇒ V/t + V/(t + 3) = V/2 ..................(1)

Dividing this equation by V, we get.

⇒1/t + 1/(t + 3) = 1/2

Taking LCM of the denominators and then solving it.

⇒ (t + 3 + t)/t(t + 3) = 1/2

Now, cross multiplying.

⇒ 2t + 6 + 2t = t² + 3t

⇒ t² + 3t - 4t - 6 = 0

⇒ t² - t - 6 = 0

⇒ t² - 3t + 2t - 6 = 0

⇒ t(t - 3) + 2(t - 3) = 0

⇒ (t + 2) (t - 3) = 0

⇒ t = - 2 or t = 3

Since, time cannot be negative.

So, time taken by tap A is 3 hours

And, time taken by tap B = 3 + 3 = 6 hours.

Hope it helps you!
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