Question

You and your roommate are moving to a city360 mi away. Your roommate drives a rental truck at a constant 50 mi/h , and you drive your car at 60 mi/h . The two of you begin the trip at the same instant. An hour after leaving, you decide to take a short break at a rest stop
If you are planning to arrive at your destination a half hour before your roommate gets there, how long can you stay at the rest stop before resuming your drive?

Answer 1

Answer:

42 minutes

Explanation:

First, let us find out the time required by the roommate, who is driving the truck, to reach the city.

We know that,

$time=\frac{distance}{speed} =\frac{360}{50} hrs=7.2hrs$

Now, you are planning to rest a bit after traveling for an hour. So,

distance covered in that 1 hour = $60mi/h\times1h=60 miles$

time required by you to cover the total distance = $\frac{360mi}{60mi/h} =6hours$

If you wish reach at the destination half an hour (0.5 h) before your roommate, you can expend a total of $7.2-0.5=6.7hours$ throughout your journey.

Hence, you can rest for  $6.7-6=0.7hours=(0.7\times60)minutes=42minutes$