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Answer:
[tex]2\frac{7}{12}[/tex] hours or 2 hours 35 minutes.
Step-by-step explanation:
A trip to Portland, Oregon from Boston will take = [tex]7\frac{3}{4}[/tex] hours
We are finished = [tex]\frac{2}{3}[/tex] of the trip
= [tex]\frac{2}{3}[/tex] × [tex]7\frac{3}{4}[/tex]
= [tex]\frac{2}{3}[/tex] × [tex]\frac{31}{4}[/tex]
= [tex]\frac{62}{12}[/tex]
= [tex]\frac{31}{6}[/tex]
= [tex]5\frac{1}{6}[/tex] hours of the trip completed.
Now we will subtract from the total time of trip to completed time of trip.
= [tex]7\frac{3}{4}[/tex] - [tex]5\frac{1}{6}[/tex]
= [tex]\frac{31}{4}[/tex] - [tex]\frac{31}{6}[/tex]
= [tex]\frac{93-62}{12}[/tex]
= [tex]\frac{31}{12}[/tex]
= [tex]2\frac{7}{12}[/tex] hours = 2.58 hours or 2 hours 35 minutes
The trip will take [tex]2\frac{7}{12}[/tex] hours