Question

You are trying to decide between two job offers. You find the best option is to take the highway to work. That route is

calculated for driving at an average speed of 65 miles per hour. You would like to keep your morning commute down to less than 30
minutes. What is the farthest distance you can travel to work within the allowable time?

Answer 1

32.5 miles

Explanation:

The average speed is 65 miles per hour.

You want to keep your commute within 30 minutes, which is HALF AN HOUR.

THus, if you can go 65 miles AN HOUR, in HALF AN HOUR, you can go max, HALF OF THAT!!

So,
`(1)/(2)*65=32.5`

Thus, you can go 32.5 miles, max

Answer 2

The farthest distance would be 32.5 miles

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}=(1)/(60)\text{ hour}`

`\implies 30\text{ minutes}=(30)/(60)=(1)/(2)\text{ hour}`

Thus,

`t\leq (1)/(2)`

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 =
`65* (1)/(2)` = 32.5 km.