Multiple choice

Pipe $A$ alone can fill one tank in $6$ hours more than it takes pipe $B$ alone to fill one tank. Together, both pipes can fill one tank in $4$ hrs. How long will it take pipe $A$ alone to fill one tank?

  1. $12$ hrs
  2. $10$ hrs
  3. $8$ hrs

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B take x hours, A takes x+6 hours. Combined rate: 1/(x+6) + 1/x = 1/4. (2x+6) / (x^2+6x) = 1/4 -> x^2+6x = 8x+24 -> x^2-2x-24 = 0 -> (x-6)(x+4) = 0. x=6. A takes x+6 = 12 hours.

AI explanation

Let the time it takes pipe B to fill the tank alone be x hours, meaning pipe A takes x plus 6 hours. Since their combined time is 4 hours, the equation for their combined rate is 1 divided by x plus 1 divided by (x plus 6) equals 1 divided by 4. Multiplying by the least common multiple of 4x(x plus 6) and rearranging yields the quadratic equation x squared minus 2x minus 24 equals 0. Factoring this gives (x minus 6)(x plus 4) equals 0, so x equals 6; since pipe A takes x plus 6 hours, it takes 6 plus 6, which equals 12 hours.

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