SOLUTION: 7. William fills 1/3 of a water bottle in 5/9 of a minute. How many bottles can he fill in a minute? Please explain this to me so I can explain it to my grandaughter who is in

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 7. William fills 1/3 of a water bottle in 5/9 of a minute. How many bottles can he fill in a minute? Please explain this to me so I can explain it to my grandaughter who is in       Log On


   

Question 1011052: 7. William fills 1/3 of a water bottle in 5/9 of a
minute. How many bottles can he fill in a
minute? Please explain this to me so I can explain it to my grandaughter who is in 7th grade, but special education student. Thanks
Found 3 solutions by stanbon, josgarithmetic, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
William fills 1/3 of a water bottle in 5/9 of a
minute. How many bottles can he fill in a
minute?
Please explain this to me so I can explain it to my grandaughter
who is in 7th grade, but special education student.
----
Not sure if your grandaughter can handle a proportion,
but that is the way to solve it.
----
Proportion:: # of bottles/time = # of bottles/time
----------
# of bottles/(1 min) = (1/3 bottle)/(5/9 min)
-----
Divide by "1" on the left side.
Divide by (5/9) on the right side.
------
Ans: # of bottles = (1/3)/(5/9) = (1/3)(9/5) = 9/15 = 3/5 of a bottle
-----
Thanks for helping your grandaughter.
Cheers,
Stan H.

Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Rate for the filling is wanted as quantity of water per 1 minute.
Quantity is not known other than as a count of "water bottle". Therefore, the unit of "bottle" is our only possible water quantity unit.

What is flow rate?
%28howMuchWater%29%2F%28howMuchTime%29.
This is a rate, wording smashed together, but should explain what the flow rate means.

Your example problem gives some data about the rate at which William fills his bottle.
How much water? 1%2F3 bottles.
How much time? .

This needs to be simplified, and if possible (yes, should be possible) form into how many bottles in ONE minute, meaning you will want a final answer showing a 1 in the denominator.

For 7th grade purposes, dividing by a fraction means the same as multiplying by its reciprocal.

%28%281%2F3%29%2F%285%2F9%29%29%28bottles%2Fminutes%29

%281%2F3%29%289%2F5%29

%281%2F3%29%28%283%2A3%29%2F5%29

%281%2A3%2A3%29%2F%283%2A5%29

highlight%283%2F5%29 bottles per minute.
This really says, or indicates "three bottles in five minutes". Maybe that is good enough for what he needs as his answer. OR this common simple fraction is also 3%2F5 bottles per minute or 0.6%2A%28bottles%2Fminute%29.

Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!
7. William fills 1/3 of a water bottle in 5/9 of a
minute. How many bottles can he fill in a
minute? Please explain this to me so I can explain it to my grandaughter who is in 7th grade, but special education student. Thanks
The easiest way to explain this is with proportions. We can say that:



%281%2F3%29%2F%285%2F9%29+=+N%2F1 ------- Substituting 1%2F3 & N (this is what's required) for number of water bottles, and 5%2F9, & 1 for amount of minutes

Since this is a proportion (fraction on either side of the equals sign), we can cross-multiply. This results in:

%285%2F9%29+%2A+N+=+%281%2F3%29+%2A+1

5N%2F9+=+1%2F3

3(5N) = 9 ------- Cross-multiply, again

15N = 9

N, or number of water bottles = 9%2F15, or highlight_green%283%2F5%29 of a water bottle