Question

Two pipes a and b can fill a tank in 36 hours and 45 hours respectively if both the pipes are opened simultaneously how much time will be taken in the sun

Answer 1

Pipe A takes 36 hours to fill a tank. Or Pipe A fills (1/36)th of the tank in 1 hour.

Pipe B takes 46 hours to fill a tank. Or Pipe B fills (1/46)th of the tank in 1 hour.

So Pipes A and B together fill (1/36)+(1/46) = (46+36)/(36*46) or (1/20.19512195)th part of the tank in 1 hour.

Hence Pipes A and B together will fill the entire tank in 20.19512195 hours.

Answer 2

Given that,

Time of pipe a = 36 hours

Time of pipe b = 45 hours

Part filled by pipe a in 1 hour = $\dfrac{1}{t_{a}}=\dfrac{1}{36}$

Part filled by pipe b in 1 hour = $\dfrac{1}{t_{b}}=\dfrac{1}{45}$

If both the pipes are opened simultaneously

Part filled by pipe (a+b) in 1 hour = $\dfrac{1}{t_{a+b}}=\dfrac{1}{36}+\dfrac{1}{45}$

We need to calculate the time

Using part filled by pipe (a+b) in 1 hour

$\dfrac{1}{t_{a+b}}=\dfrac{1}{36}+\dfrac{1}{45}$

$\dfrac{1}{t_{a+b}}=\dfrac{45+36}{45\times36}$

$\dfrac{1}{t_{a+b}}=\dfrac{1}{20}$

$t_{a+b}=20\ hours$

Hence, Both the pipes together will fill the tank in 20 hours.