WORD PROBLEM

Question

You are watering a garden using two hoses. one of the hoses has a kink in it that causes it to release water at one-third of the speed of the other. Together, the two hoses take 3 hours to water the garden. WHich of the following expressions models this scenario?

 

1. 3x + x = 3

2. x/3 + 1/x = 1/3

3. 1/x + 3/x = 1/3

 

Answer 1

The VERY IMPORTANT piece of information in this and other "combination" problems is that the values seem to be inverted. That is, "1 garden is watered in 3 hours" rather than "3 hours to water the garden."

 

Rate of first hose         +       Rate of second hose      =    Combined rate

 (1 garden)/(t/3 hours)    +     (1 garden)/(t hours)    =    (1 garden/(3 hours)

    3/t                            +          1/t                         = 1/3

 

This resembles (3).

 

1/x + 3/x = 1/3

 3 + 9 = x

   12 = x

and

   (1/3) x = 4

 

So, together, a hose that waters at the rate of 12 hours per garden with a hose that waters at the rate of 4 hours per garden can water one garden in 3 hours.        [ in 12 hours, that is 1+3 gardens;  that is, 12 hours per 4 gardens, or 3 hours for 1 garden, but written as "1 garden in 3 hours"].