Question

it takes 24 hours to fill a swimming pool using two pipes. if the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours . only half of the pool is filled. how long would each pipe take to fill the swimming pool.?

Answer 1

Answer:

40 hours and 60 hours

Step-by-step explanation:

Hi,

Let 'x' be the number of hours larger pipe alone takes to fill a

pool

⇒ In 1 hr, larger pipe fills 1/x of the pool

Let 'y' be the number of hours smaller pipe alone takes to fill a

pool

⇒ In 1 hr, smaller pipe fills 1/y of the pool

Given both takes 24 hours to fill a pool

⇒ 1/x + 1/y = 1/24-----(1)

Also, given that if larger piper is used for 8 hours and smaller

pipe for 18 hours, half of the pool is filled

⇒ 8/x + 18/y = 1/2 ----(2)

Using  (2) - 8(1), we can find that

10/y = 1/6

⇒ y = 60 and x = 40 hours

Hence larger diameter pipe takes 40 hours and smaller

diameter pipe takes 60 hours to fill a swimming pool if they are

open alone

Hope, it helped !

Answer 2

Answer:

larger pipe can do in 40 hours and smaller pipe would take 60 hours

Step-by-step explanation:

Let time taken by large pie  be xhrs

Let time taken by smaller pipe  be y hrs in one hour

larger pipe can fill =1/x  In one hour smaller pipe can fill=1/y

Equations :

1/x+1/y=1/24

8/x +18/y=1/2

let us assume 1/x=a and 1/y=b

a+b=1/24------------1

8a+18b=1/2-------------2

multiply equation 1 by 8

8a+8b=1/3---------3

8a+18b=1/2------------4

subtract 3 -4 we get

8b-18b=1/3-1/2

10b=2-3/6

-10b=-1/6

b=1/60

y=60

Substituting in equation 1  

we get

a+1/60=1/24

a=1/24-1/60

x=40

Hence larger pipe can do in 40 hours and smaller pipe would take 60 hours