Using proportions, it is found that it will take Michael 2.625 hours to drive to his mother's house.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In 1 hour and 45 minutes, which is equivalent in hours to [tex]1 + \frac{3}{4} = \frac{7}{4}[/tex], he is two-thirds of the way. How long it takes him to reach 100% = 1 of the way? The rule of three is given by:
[tex]\frac{7}{4}[/tex] hours - [tex]\frac{2}{3}[/tex] way.
x hours - 1 way
Applying cross multiplication:
[tex]\frac{2}{3}x = \frac{7}{4}[/tex]
[tex]2x = \frac{21}{4}[/tex]
[tex]x = \frac{21}{8}[/tex]
x = 2.625.
It will take Michael 2.625 hours to drive to his mother's house.
More can be learned about proportions at https://brainly.com/question/24372153
