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Answer:
When the truck is full: [tex]g_{mf} = \frac{m}{8}[/tex]
When the truck is empty: [tex]g_{me} = \frac{m}{9.6}[/tex]
Step-by-step explanation:
When the truck is full for every eight miles traveled by the vehicle, there is a cost of one gallon of fuel, therefore for every mile the cost is one eight of a gallon, with this information we can create the following expression:
[tex]g_{mf} = \frac{m}{8}[/tex]
Where m is the number of miles traveled by the truck.
When the vehicle is empty, it's performance improves by 20 %, which means that for the same amount of fuel it'll travel a distance 120% of the previous one. Therefore we need to multiply 1.2 on the denominator of the last expression:
[tex]g_{me} = \frac{m}{8*1.2}\\\\g_{me} = \frac{m}{9.6}[/tex]
The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex]
Given that,
A long-distance delivery truck averages 8 miles per gallon when the truck is full.
The miles per gallon improve by 20% when the truck is empty.
We have to determine,
Which expression represents the amount of gasoline used (g) in terms of the number of miles driven when full (mf) and the number of miles driven when empty (me).
According to the question,
The amount of gasoline used (g) in terms of the number of miles driven when full (mf),
And The distance delivery truck averages 8 miles per gallon when the truck is full.
The amount of gasoline when the truck is full is represented as,
[tex]m_f = \dfrac{m}{8}[/tex]
Then,
The miles per gallon improve by 20% when the truck is empty.
The number of miles driven when empty is represented as,
[tex]m_e = \dfrac{m}{8 + 8 \times 0.20}\\\\m_e = \dfrac{m}{8+ 1.6}\\\\m_e = \dfrac{m}{9.6}[/tex]
Hence, The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex].
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