Question

A cistern can be filled by two pipes in 100/3 minutes . If the larger pipe takes 15 minutes less than that he smalles to fill the cistern we need to find in what time it will be filled by the pipe individually​

Answer 1

Answer:

Step-by-step explanation:

Given  

A cistern can be filled by two pipes in 100/3 minutes . If the larger pipe takes 15 minutes less than that he smallest to fill the cistern we need to find in what time it will be filled by the pipe individually​

ANSWER

Let the pipes be p1 and p2 and V be the volume of the cistern.

Now p1 will fill the cistern in t1 minutes and

     P2 will fill the cistern in t2 minutes, time taken is 100/3 minutes.

Also t1 = t2 + 15

(V/t1 + V/t2) x 100/3 = V

1/t2 + 15 + 1/t2 = 3/100

100(2 t2 + 15) = 3 t2 (t2 + 15)

- 3t^2 + 155 t2 + 1500 = 0

3 t^2 – 155 t2 – 1500 = 0

So applying the formula we get

    x = - b ± √b^2 – 4 a c / 2a

  t2 = - (-155 ) ± √- 155^2 – 4(3)(- 1500) /  2(3)

  t2 = 155 ± √42,025 / 6

  t2 = 155 + 205 / 6 and t2 = 155 – 205 /6

 t2 = 60 and t2 = - 8.334

Now time taken by p1 to fill the cistern is t2 + 15 = 60 + 15 = 75 minutes or 1 hour 15 minutes.

Time taken by p2 to fill the cistern is 60 minutes or 1 hour.