Answer:
The farthest distance would be 32.5 miles
Step-by-step explanation:
Given,
Speed = 65 miles per hour,
If t represents the time ( in hours ) taken in travelling,
Since, time has to commute down less than 30 minutes,
Also, 1 hour = 60 minutes,
![\implies 1\text{ minute}=\frac{1}{60}\text{ hour}](https://tex.z-dn.net/?f=%5Cimplies%201%5Ctext%7B%20minute%7D%3D%5Cfrac%7B1%7D%7B60%7D%5Ctext%7B%20hour%7D)
![\implies 30\text{ minutes}=\frac{30}{60}=\frac{1}{2}\text{ hour}](https://tex.z-dn.net/?f=%5Cimplies%2030%5Ctext%7B%20minutes%7D%3D%5Cfrac%7B30%7D%7B60%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7B%20hour%7D)
Thus,
![t\leq \frac{1}{2}](https://tex.z-dn.net/?f=t%5Cleq%20%5Cfrac%7B1%7D%7B2%7D)
i.e. the highest time taken = 1/2 hours,
We know that,
Distance = speed × time,
∵ Distance ∝ time,
⇒ Distance will farthest for largest time taken,
Hence, the farthest distance =
= 32.5 km.