If three pipes are all opened, they can fill an empty swimming pool in 3 hours. the largest pipe alone takes one third the time that the smallest pipe takes and half the time the other pipe takes. how long would it takes each pipe to fill the pool by itself?

It will take the largest pipe 5.5 hours to fill the swimming pool alone.

It will take the smallest pipe 16.5 hrs to fill the swimming pool alone.

It will take the other pipe 11 hours to fill the pool alone.

Step-by-step explanation: let time needed to fill the swimming pool by the largest pipe be x ... eq (1)

Let time needed to fill the swimming pool by the smallest pipe be 3x ... eq(2)

Let time needed to fill the swimming pool by the other pipe be 2x ...eq(3)

The job to be done (to fill a swimming pool) be 3/x +3/3x+3/2x=1 ... eq(4)

Multiply 6x on both sides you will get:

6(3)+2(3)+3(3)=6x

18+6+9=6x

33=6x

33/6=x

X=5.5hours

Substitute x=5.5 into EQ 2 and 3

3x=3×5.5=16.5hours

2x=2×5.5=11hours

Check: substitute the value of x into eq3/5.5+3/16.5+3/11

0.545+0.182+0.273=0.9997=1

correct answers below: