Math, asked by sandeep7702, 1 year ago

If two pipes function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir? 1 point

Answers

Answered by amitnrw
7

Answer:

Second Pipe fill reservoir in 30 Hrs

Step-by-step explanation:

two pipes  simultaneously fill  the reservoir  in 12 hours

two pipes  simultaneously in 1hr  fill  the reservoir = 1/12

Let say one pipe fill the reservoir  in x hr

Second pipe fills reservoir  in x + 10 hr  ( as pipe one is 10 hr faster)

Pipe one fill reservoir in 1 hr = 1/x

Second pipe fill reservoir in 1 hr = 1/(x+10)

1/x  + 1/(x+10)  = 1/12

Multiplying both sides by 12x(x+10)

=> 12(x + 10)  + 12x = x(x+10)

=> 12x + 120 + 12x = x² + 10x

=> 0 = x² - 14x -120

=> x² - 14x -120 = 0

=> x² - 20x + 6x - 120 = 0

=> x(x-20) + 6(x-20) =0

=> (x+6)(x-20) = 0

x = 20

pipe one fill reservoir in 20 Hrs

Second Pipe fill reservoir in 20 + 10 = 30 Hrs

Answered by mathsdude85
0

SOLUTION :  

Let the faster pipe fill the reservoir in x h.

Then, the  slower pipe the reservoir in (x + 10) h

In 1 hour the faster pipe fills the portion of the reservoir : 1/x  

In 12 hour the faster pipe fills the portion of the reservoir : 12 ×  1/x  = 12/x

In 1 hour the slower pipe fills the portion of the reservoir : 1/(x + 10)

In 12 hour the faster pipe fills the portion of the reservoir : 12 × 1/(x + 10) = 12/(x +10)

A.T.Q  

12/x + 12/(x +10) = 1

12(1/x + 1/(x + 10) ) = 1

1/x + 1/(x + 10) = 1/12

(x + 10 + x ) / [x(x + 10)] = 1/12  

[By taking LCM]

2x +10 /(x² + 10x) = 1/12  

x² + 10x = 12(2x +10)

x² + 10x = 24x + 120

x² + 10x - 24x - 120 = 0

x² - 14x - 120 = 0

x² + 6x - 20x - 120 = 0

[By splitting middle term]

x(x + 6) - 20(x + 6) = 0

(x - 20) (x + 6) = 0

(x - 20) or  (x + 6) = 0

x = 20  or  x = - 6

Since, time cannot be negative, so x ≠ - 6  

Therefore, x = 20  

The faster pipe takes 20 hours to fill the reservoir

Hence, the slower pipe (second) takes (x + 20) = 30 hours to fill the reservoir.

HOPE THIS ANSWER WILL HELP YOU…...

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