[tex]\huge\boxed{{\textsf{90 minutes}}}[/tex]
We know that Mike's speed is [tex]\dfrac{10\ \text{miles}}{60\ \text{minutes}}[/tex] since there are [tex]60[/tex] minutes in an hour, and we know that MIke needs to travel [tex]15[/tex] miles. We'll model this using fractions:
[tex]\dfrac{10\ \text{miles}}{60\ \text{minutes}}=\dfrac{15\ \text{miles}}{x\ \text{minutes}}[/tex]
We can see that there is a [tex]2:3[/tex] ratio here, so we'll divide the left fraction by [tex]2[/tex] and multiply it by [tex]3[/tex] to get the right fraction.
[tex]\dfrac{10}{60}\Rightarrow\dfrac{5}{30}\Rightarrow\dfrac{15\ \text{miles}}{\boxed{90\ \text{minutes}}}[/tex]
