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Two Pipes Running Together Can Fill a Tank in `11 1/9` Minutes. If One Pipe Takes 5 Minutes More than the Other to Fill the Tank Separately, Find the Time in Which Each Pipe Would Fill the Tank Separately. - CBSE Class 10 - Mathematics

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Question

Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Solution

Let the first pipe takes x minutes to fill the tank. Then the second pipe will takes (x + 5)minutes to fill the tank.

Since, the first pipe takes x minutes to fill the tank.

Therefore, portion of the tank filled by the first pipe in one minutes = 1/x

So, portion of the tank filled by the first pipe in `11 1/9` minutes `=100/(9x)`

Similarly,

Portion of the tank filled by the second pipe in `11 1/9` minutes `=100/(9(x+5))`

It is given that the tank is filled in `11 1/9`minutes.

So,

`100/(9x)+100(9(x+5))=1`

`(100(x+5)+100x)/(9x(x+5))=1`

100x + 500 + 100x = 9x2 - 45x

9x2 + 45x - 200x - 500 = 0

9x2 - 155x - 500 = 0

9x2 - 180x + 25x - 500 = 0

9x(x - 20) + 25(x - 20) = 0

(x - 20)(9x + 25) = 0

x - 20 = 0

x = 20

Or

9x + 25 = 0

9x = -25

x = -25/9

But, x cannot be negative.

Therefore, when x = 20 then

x + 5 = 20 + 5 = 25

Hence, the first water tape will takes 20 min to fill the tank, and the second water tape will take 25 min to fill the tank.

  Is there an error in this question or solution?

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Solution Two Pipes Running Together Can Fill a Tank in `11 1/9` Minutes. If One Pipe Takes 5 Minutes More than the Other to Fill the Tank Separately, Find the Time in Which Each Pipe Would Fill the Tank Separately. Concept: Solutions of Quadratic Equations by Factorization.
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