Question

One fill pipe A is 10 times faster than second fill pipe B. If B can fill a cisten in 55 mins, then find the time when the cistern will be full if both fill pipes are opened together.​

Answer 1

Step-by-step explanation:

A is 10 times faster than B

B alone can fill a cistern in 55 mins

A is 55*10 = 550

converting into minutes 550/60

A can fill a cistern in 9 mins 17 sec.

if both are opened at a time then time taken to fill a cistern is

9.17+55/2 = 32mins and 08 seconds.

Answer 2

Given,

Speed of fill pipe A = 10 × the speed of the fill pipe B.

Time taken by fill pipe B to fill a cistern = 55 mins

To find,

The time taken to fill the cistern if both fill pipes are opened together.

Solution,

We can simply solve this mathematical problem using the following process:

Let the capacity of the cistern be x liters and the time taken to fill the cistern if both fill pipes are opened together is y mins.

Mathematically,

The speed of a fill pipe is defined as the amount of water delivered in unit time.

=> speed of a fill pipe = (amount of water delivered)/(time taken) = (capacity of the container)/(total time taken to fill the container)

=> (amount of water delivered)/(time taken) = (speed of the fill pipe)×(time taken)

{Statement-1}

Now, according to the question;

The speed of a fill pipe B = (x/55) L/min

The speed of a fill pipe A = (10x/55) L/min

Now, according to the question;

(Amount of water poured by fill pipe A) + (Amount of water poured by fill pipe B) = total capacity of the cistern

=> y mins × (10x/55) L/min + y mins × (x/55) L/min = x L

{according to statement-1}

=> y(10/55 + 1/55) = 1

=> y(11/55) = 1

=> y(1/5) = 1

=> y = 5 mins

=> time taken to fill the cistern if both fill pipes are opened together = 5 mins

Hence, the time taken to fill the cistern if both fill pipes are opened together is equal to 5 mins.