Question

It takes 24 hours to fill a swimming pool using two pipes if the pipe of larger diameter is used for 8hours and the pipe of 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:

smaller pipe will take 40 hrs to fill the swimming pool and larger pipe will take 60 hrs to fill the swimming pool.

Step-by-step explanation:

Let us consider,

smaller pipe take x hrs to fill

larger pipe take y hrs to fill

then,

=>  (24/x)+ (24/y)=1 (filled full)

and

=> (8/x)+(18/y)= 1/2 (filled half)

Let 1/x= a and 1/y =b

Then,

24a+24b= 1     -------equation (1)

and 8a+18b= 1/2    

Multiplying equation by 3

24a+54b= 3/2      -------equation (2)

Equating equation (1) and (2)

30b= (3/2)-(1/2)

30b= 1/2

b= 1/60

putting the value of b in equation (1)

24a+ 24(1/60)= 1

24a= 1-2/5

a= 3/(24x5)

a= 1/40

x= 40 hrs

y= 60 hrs

smaller pipe will take 40 hrs to fill the swimming pool and larger pipe will take 60 hrs to fill the swimming pool.