Question

Two pipes working together can fill the tank in 35 minutes. If the larger pipe alone can fill the tank in 24 minutes less than the time taken by the smaller pipe, then find the time taken by each pipe working alone to fill the tank.
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Answer 1

Answer:

84 & 60 Mins

Step-by-step explanation:

Let say Smaller Pipe Fill the Tank in  P mins

Then Larger Pipe  fills the tank in P - 24  Mins

Tank filled in 1 Min by Smaller Pipe = 1/P

Tank filled by Larger pipe in 1 Min = 1/(P - 24)

Tank filled by both pipe together in 1 Min =  1/P + 1/(P - 24)

Both pipe together can fill tank in 35 mins

=> tank filled in 1 Min = 1/35

=> 1/P + 1/(P - 24) = 1/35

=> 35 ( P - 24 + P) = P(P - 24)

=> 70P - 35 * 24  = P² - 24P

=> P² - 94P  + 35 * 24  = 0

=> P² - 84P - 10P  + 35 * 24 = 0

=> P (P - 84) - 10(P - 84)  = 0

=> (P - 10)(P-84) = 0

=> P = 10 or 84

Larger Pipe fills the tank in P - 24  Mins = 10 - 24 = -14 not possible

Hence Tank Filled by Smaller pipe  in 84 mins

& Tank fille d by Larger pipe in 84-24 = 60 min

Answer 2

Smaller Pipe Fill in x

Larger Pipe fills in x - 24

Tank filled by both pipe together = 1/x + 1/(x - 24)

1/x + 1/(x - 24) = 1/35

35(x - 24 + x) = x(x - 24)

70x - 35 * 24 = x² - 24x

x² - 94x + 35 * 24 = 0

x² - 84x - 10x + 35 * 24 = 0

x(x - 84) - 10(x - 84) = 0

(x - 10)(x-84) = 0

x = 10 ; 84

Larger Pipe fills the tank in x - 24 Mins = 10 - 24 = -14 Not Possible

Smaller pipe fills the tank in 84 mins

Larger pipe in = 60 min