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Charlie is driving to Boston. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Charlie has 49 miles to his destination after 15 minutes of driving, and he has 32.2 miles to his destination after 39 minutes of driving. How many miles will he have to his destination after 47 minutes of driving

Respuesta :

Answer:26.6 miles

Step-by-step explanation:

Given

Charlie distance to his destination  is a linear function of total driving time

suppose distance d is related to time t as

[tex]d=mt+c\quad \ldots(i)[/tex]

at [tex]d=49\ miles[/tex] after [tex]t=15\ min[/tex]

Substitute in (i)

[tex]49=m(15)+c\quad \ldots(ii)[/tex]

at [tex]d=32.2\ miles[/tex] after [tex]t=39\ min[/tex]

[tex]32.2=m(39)+c\quad \ldots(iii)[/tex]

Solving (ii) and (iii) we get

[tex]m=-0.7[/tex]

substitute in eq (ii) we get

[tex]c=59.5[/tex]

so after [tex]t=47\ min[/tex]  

[tex]d=(-0.7)47+59.5[/tex]

[tex]d=59.5-32.9=26.6\ miles[/tex]

So 26.6 miles is left to travel after 47 minutes

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