A hose can fill a swimming pool in 4 hours. Another hose needs 9 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

Answer 1

Lets think of the situation. It doesn't tell you how big the pool but you can make up a value. To make it easier use a number that it a multiple of both 4 and 9. In this case it would be 36.

Okay say the pools need 36 gallons of water to be full. To find the rate for each hose divide
total amount needed/time

Hose 1: 36/4=9
Hose 2: 36/9=4

Hose 1 rate is 9 gallons per hour and Hose 2 rate is 4 gallons per hour

Add the 2 together 9+4=13 gallons per hour

Now divide 36 by 13

36/13= 2.77 Hours

Is this clear? I know it's long winded but I wanted to explain the full process.

Answer 2

that helps a lot thank you

Answer 3

or,

1/4 + 1/(x+9) = 1/x
x = 3

so, the 2nd hose takes 12 hours

check: in 1 hour, the two hoses fill
1/4 + 1/12 = 1/3 of the pool.