Work word problems

Question

One hose can fill a swimming pool in 18 hours while a second hose can fill pool same pool in 14 hours. How long would it take both hoses together to fill the pool?

 

 

 

 

 

Answer 1

Hey Maggie!

The 8-hour answer makes sense physically: if you have 2 hoses each at the rate of a pool in 18 hours, it logically takes half the time or 9 hrs. If you have 2 hoses each at the 14-hr rate, pool filling takes 7 hrs. Since your problem has a mix, you expect an answer between 7-9 hrs, and 8 hrs sounds very right.  Regards :)

Answer 2

Great problem. What you need to think about is how much water leaves each hose per hour.

The first hose would fill 1/18 of the pool in one hour, since it takes 18 hours to fill the whole pool.

The second hose would fill 1/14 of the pool in one hour.

Let's use the variable t for time in hours. The amount of water from hose 1 will be (1/18)(t), and the amount of water from hose 2 will be (1/14)(t). Both together will add up to 1 pool of water after the value for t which fills the pool.

So, t/18 + t/14 = 1

Solve for t. (we need a common denominator)

18 = 9(2)   14= 7(2)  Lowest common denominator is 9(7)(2) = 126

7t/126 + 9t/126 = 1

16t/126 = 1

16t = 126 

t = 7.875 hours or 7 hours, 52 minutes and 30 seconds

0.875 hours (60 minutes/hour) = 52.5 minutes