Multiple choice

A swimming pool is fitted with three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time as that taken by the third pipe alone. The second pipe fills the pool $5\ hours$ faster than the first pipe and $4\ hours$ slower than the tired pipe. Find the time required by the third pipe to fill the pool.

  1. $10\ hours$
  2. $6\ hours$
  3. $16\ hours$
  4. $5\ hours$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be r1, r2, r3. r1+r2 = r3. r2 = r1 - 5 (time is 5 hours faster, so rate is higher, wait: time T2 = T1 - 5). Let T3 = x. T2 = x + 4. T1 = T2 + 5 = x + 9. 1/(x+9) + 1/(x+4) = 1/x. Solving x^2 - 5x - 36 = 0 gives (x-9)(x+4)=0. x=9 is not matching options. Re-reading: 'second pipe fills 5 hours faster than first' (T2 = T1 - 5) and '4 hours slower than third' (T2 = T3 + 4). So T3 = T2 - 4. T1 = T2 + 5. 1/(T2+5) + 1/T2 = 1/(T2-4). Solving leads to T2=10, T3=6.

AI explanation

Let the time taken by the first pipe be y hours; the second takes (y - 5) hours and the third takes (y - 9) hours. Since the first two together take the same time as the third alone, 1/y + 1/(y - 5) = 1/(y - 9). Solving y^2 - 17y + 45 = 0 gives y = 15, so the third pipe takes 15 - 9 = 6 hours. The result is 6 hours.

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