Justin drove 143.6 miles
Explanation:This forms a right-angles triangle
The distance between the grandmother and the aunty's place = 175 miles
Distance traveled by Kelsey to the grandmother's house = 100miles
Let the distance by Justin to his aunt's place = x
Using the Pythagora's theorem
[tex]\begin{gathered} 175^2=100^2+x^2 \\ x^2=175^2-100^2 \\ x^2=20625 \\ x=\lor20625 \\ x=143.6\text{ miles} \end{gathered}[/tex]Justin drove 143.6 miles