You and your roommate are moving to a city 380 mimi away. Your roommate drives a rental truck at a constant 55 mi/hmi/h, and you drive your car at 65 mi/hmi/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? Express your answer using two significant figures. t = Min

You can stay at the rest stop for 36 min.

Explanation:

Hi there!

First, let's calculate how much does it take to your roommate to reach the destination. For this we use the equation of traveled distance at constant speed:

x = v · t

Where:

x = traveled distance.

v = speed.

t = time.

Solving for t:

x/v = t

380 mi / 55 mi/h = t

t = 6.9 h

It takes your roommate 6.9 h to reach your destination.

Now, let's see how much distance do you travel in an hour before stopping:

x = v · t

x = 65 mi/h · 1 h

x = 65 mi

And now let's see in how much time you can do the rest of the trip:

x = 380 mi - 65 mi = 315 mi

x/v = t

315 mi / 65 mi/h = t

t = 4.8 h

Then, you will travel for (1 h + 4.8 h) 5.8 h. If you want to reach your destination 0.5 h before your roommate (that is, in (6.9 h - 0.5 h) 6.4 h after departing), you can stay at the rest stop for (6.4 h - 5.8 h) 0.6 h. In minutes:

0.6 h · (60 min / h) = 36 min

You can stay at the rest stop for 36 min.