Question

hey guys pls help me with this one... will mark the best answer brainliest

Answer 1

Answer:

28 minutes, 21 minutes

Step-by-step explanation:

Let the time taken by tap B to fill the tank is 'x' minutes.

∴ Part filled by tank B in 1 minute = (1/x).

Given that A takes 7 minutes more than tap B.

Then, the time take by tap A is 'x + 7' minutes.

∴ Part filled by tan A in 1 minute = (1/x + 7).

Part of the tank filled by (A + B) in 1-minute = (1/x) + (1/x + 7)

= [x + 7 + x]/[x(x + 7]

= [2x + 7]/[x² + 7x]

∴ Total time = [x² + 7x]/[2x + 7]

Given that Tap A takes 16 minutes more than the time taken by both.

⇒ x + 7 = {[x² + 7x]/[2x + 7]} + 16

⇒ (2x + 7)(x + 7) = (x² + 7x) + 16(2x + 7)

⇒ 2x² + 14x + 7x + 49 = x² + 7x + 32x + 112

⇒ 2x² + 21x + 49 = x² + 39x + 112

⇒ x² - 18x - 63 = 0

⇒ x² - 21x + 3x - 63 = 0

⇒ x(x - 21) + 3(x - 21) = 0

⇒ (x - 21)(x + 3) = 0

⇒ x = 21, -3{∴Cannot be negative}

⇒ x = 21.

Now:

⇒ x + 7

⇒ 28.

Therefore:

⇒ Time taken by tap A = 28 minutes.

⇒ Time taken by tap B = 21 minutes.

Hope it helps!