Question

A swimming pool can be filled by any one of four different hosepipes in 8, 10, 16 or 20 hours. How long will it take to fill the pool if all four hosepipes are used at the same time, without reducing the water pressure? Express your answer in hours and minutes, rounded to the nearest minute.

Answer 1

Let us take these 4 different pipes be A, B, C and D

A takes 8 hours

B takes 10 hours

C takes 16 hours

D takes 20 hours

Now we have to find how much time will it take to fill the swimming pool if all 4 pipes are opened together.

So let that time=x hours

Now 1/x =(1/A)+(1/B)+(1/C)+(1/D)

1/x=(1/8)+(1/10)+(1/16)+(1/20)

1/x=(10+8+5+4)/80 {taking LCM on RHS}

1/x= 27/80

or x=80/27

Now x= 2(26/27) write in a mixed fraction form

So converting 26/27 into minutes 26*60/27= 57.77 =58 minutes

So total time taken is x= 2 hours 58 minutes