Please help, Don't know how to do this word problem.

Question

With water from one hose, a swimming pool can be filled in 8 hours. A second, larger hose used alone can fill the pool in 5 hours. How long would it take to fill the pool if not hoses were used simultaneously

Answer 1

This problem can be solved by dividing the product of the two times by the sum of them.

 

(8*5)/(8+5), which is 40/13 or approx 3.08 hours. 

Answer 2

Since you are in a "College Algebra" class, I will solve the problem algebraically.  

 

Let x = Time it takes to fill the pool if both hoses are used

 

1/8 = amount of pool filled by the first hose in one hour

1/5 = amount of pool filled by the second hose in one hour

1/x = amount of pool filled by both hoses in one hour

 

Then, 1/8 + 1/5 = 1/x

 

Multiply both sides by the LCD, 40x:  5x + 8x = 40

 

                                                          13x = 40

 

                                                             x = 40/13 hours