Question

I would mark the correct answer brainliest.​

Answer 1

Answer:

50 minutes, 40 minutes

Step-by-step explanation:

Let the time taken by the smaller tap to fill tank = x hours.

So, volume of tank filled by smaller tap in 1 hour = (1/x).

Given that tap of larger diameter takes 10 minutes less than smaller one.

So, volume of tank filled by larger tap in 1 hour = (1/x - 10).

Given, Two water taps together can fill in 22 (2/9) minutes = (200/9) mins

⇒ 200/9x + 200/9(x - 1) = 1

⇒ 200/9[1/x + 1/x - 1] = 1

⇒ 200/9[2x - 10/x²  - 10x] = 1

⇒ (2x - 10)/(x² - 10x) = 9/200

⇒ 200(2x - 10) = 9(x² - 10x)

⇒ 400x - 2000 = 9x² - 90x

⇒ 9x² - 490x + 2000 = 0

⇒ 9x² - 450x - 40x + 2000 = 0

⇒ 9x(x - 50) - 40(x - 50) = 0

⇒ (x - 50)(9x - 40) = 0

⇒ x = 50, x = 40/9{Neglected}

⇒ x = 50.

When x = 50:

⇒ x - 10

⇒ 50 - 10

⇒ 40.

Therefore:

Time taken by the smaller tap = 50 minutes.

Time taken by the larger tap = 40 minutes.

Hope it helps!

Answer 2

You can solve the value of x and you get 40 and 50 minutes.