Question

the water tap Atakes 7 minutes more than water tap B for filling up a tank with water. The tap A takes 16 minutes more than the time taken by both the taps together to fill the tank. find the time each tap alone would take to fill the tank

Answer 1

Answer:

Tap A takes 28 min to fill a tank.

Tap B takes 21 min to fill a tank.

Step-by-step explanation:

Say tap A gives water at the rate of a min/tank and tap B at the rate b min/tank.

We are told that a = b + 7.

Now A's rate can also be expresses as (1/a) tanks/min and B's rate as (1/b) tanks/min.  So when the two taps are working together, the release water at the rate of

( 1/a  +  1/b ) tanks / min.

In minutes per tank, this is

1 / ( 1/a + 1/b )  min / tank

=  ab / ( a + b )   min / tank.

We are told that tap A takes 16 minutes longer for a tank than both taps combined, so

a = ab / ( a + b )  +  16

=>  a ( a + b ) = ab + 16 ( a + b )

=>  a² + ab = ab + 16a + 16b

=> a² = 16a + 16 ( a - 7 )    (since we know that b = a - 7)

=> a² - 32a = -7 × 16

=> ( a - 16 )² = 16 × 16  -  7 × 16 = 9 × 16

=> a - 16 = ± 3 × 4 = ±12

=> a = 16 ± 12 = 28 or 4.

But a = b + 7 and b cannot be negative, so we conclude that a = 28 and b = a - 7 = 21.

Answer 2

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!