two pipes running together can fill a tank in 100/9 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.

 

Asked by susanta.rkl | 18th Aug, 2018, 08:03: PM

Expert Answer:

begin mathsize 16px style Let space one space of space the space pipe space take space straight x space minutes space to space then space the space slower space pipe space will space take space left parenthesis straight x plus 5 right parenthesis space minutes.
Time space taken space by space both space pipe space to space fill space the space tank equals 100 over 9 minutes.
Portion space of space tank space filled space by space faster space pipe space in space 1 minute equals 1 over straight x
Portion space of space tank space filled space by space faster space pipe space in 1 minute equals fraction numerator 1 over denominator 1 space plus space 5 end fraction
Portion space of space tank space filled space by space both space pipe space in space one 1 minute equals fraction numerator 1 over denominator begin display style 100 over 9 end style end fraction equals 9 over 100
1 over straight x space plus space fraction numerator 1 over denominator straight x space plus space 5 space end fraction equals space 9 over 100
rightwards double arrow fraction numerator straight x plus 5 plus straight x over denominator straight x left parenthesis straight x plus 5 right parenthesis end fraction space equals 9 over 100 space
rightwards double arrow fraction numerator 2 straight x plus 5 over denominator straight x 2 plus 5 straight x end fraction space equals 9 over 100 space
rightwards double arrow 200 straight x plus 500 equals 9 straight x squared plus 45 straight x
rightwards double arrow 9 straight x squared plus 45 straight x minus 200 straight x minus 500 equals 0
rightwards double arrow 9 straight x squared minus 155 straight x minus 500 equals 0
rightwards double arrow 9 straight x squared minus 180 straight x plus 25 straight x minus 500 equals 0
rightwards double arrow 9 straight x left parenthesis straight x minus 20 right parenthesis plus 25 left parenthesis straight x minus 20 right parenthesis equals 0
rightwards double arrow left parenthesis 9 straight x plus 25 right parenthesis left parenthesis straight x minus 20 right parenthesis equals 0
rightwards double arrow straight x equals fraction numerator negative 25 over denominator 9 end fraction space and space straight x equals 20
But space straight x space can apostrophe straight t space be space negative space as space it space represents space time.
Therefor comma straight X equals 20 space minutes.
Time space taken space by space faster space pipe space to space fill space the space tank equals 20 minutes.
Time space taken space by space slower space pipe space to space fill space the space tank equals 20 plus 5 equals 25 space minutes. end style

Answered by Yasmeen Khan | 20th Aug, 2018, 10:40: AM

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