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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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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.
Solved and carefully/thoroughly explained.
Happy learning (!)