Question 1195425: 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
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
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
~~~~~~~~~~~~~~~~
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 (!)
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