Question 1195425
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G=450-3.25t
Amaka planted tomatoes in her garden. The equation above relates the area G,
in square feet, of the unplanted space in the garden to the number of minutes
t after Amaka began planting.
Amaka’s friend Juanita began planting her 375-square-foot garden with tomatoes 
at the same time as Amaka began, but Juanita worked at one-half Amaka’s rate. 
If the area of unplanted space in each garden was the same m minutes 
after both Amaka and Juanita began planting, which of the following is closest 
to the value of m?
A) 40
B) 43
C) 46
D) 50
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<pre>
From the given equation, Amaka's rate of work is planting 3.25 square feet per minute.


Hence, Juanita's rate of work is half of it, or 3.25/2 = 1.625 square feet per minute.


So, the remaining area for Juanita is this equation

    G = 375 - 1.625.



The problem asks to find minutes, when the remaining areas are the same

    450 - 3.25t = 375 - 1.625t.


Collect the terms wit "t" in the right side; collect the constant term in the left side

    450 - 375 = 3.25t - 1.625t


Simplify and find minutes

      75      = 1.625t

       t      = 75/1.625 = 46.15 minutes.


The closest number from the answer list is option (C) 46 minutes.
</pre>

Solved and carefully/thoroughly explained.



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