Question

It take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, onlyhalf of the pool is filled. How long would it take for each pipe to fill the pool separately

Answer 1

let large pipe takes x hours to fill the tank

so in 4 hours large pipe fills = 4/x tank

and small pipe takes y hours to fill the tank

so in 9 hours small pipe fills = 9/y tank

4/x + 9/y = 1/2

9x + 4y / xy = 1/2

18x + 8y = xy ----- 1


also

1/x + 1/y =1/12

x + y / xy = 1/12

12x + 12y = xy ---- 2

by eq 1 and eq 2

18x + 8y = 12x + 12y

6x = 4y

3x = 2y

12x = 8y

putting this value in eq 1

18x + 12x = xy

30x = xy

y = 30

so x = 20


large pipe takes 20 hours and small pipe takes 30 hours

Answer 2

Answer:

The pipe of larger diameter alone can fill the pool in 20 hours and the pipe of smaller diameter alone can fill the pool in 30 hours.