Multiple choice

Two pipes A and B together can fill a cistern in $4$ hours. Had they been opened separately, then B would have taken $6$ hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

  1. $1$ hour
  2. $2$ hours
  3. $6$ hours
  4. $8$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A take x hours, then B takes x + 6 hours. Together, 1/x + 1/(x+6) = 1/4. Solving 4(x+6 + x) = x(x+6) gives 8x + 24 = x^2 + 6x, or x^2 - 2x - 24 = 0. Factoring gives (x-6)(x+4) = 0. Since time is positive, x = 6.

AI explanation

Let pipe A take x hours, so pipe B takes x + 6 hours. Using the combined work formula, 1 divided by x plus 1 divided by x + 6 equals 1 divided by 4. Multiplying by 4x(x + 6) gives 4x + 24 plus 4x equals x squared + 6x, which simplifies to x squared minus 2x minus 24 equals 0. Solving this quadratic equation gives x = 6 hours.

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