Answer:
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.
You can rest for 0.56 hours before resuming your drive and still arrive 30 minutes earlier.
Speed
Speed is the ratio of total distance to total time taken. It is given by:
Speed = distance / time
For the rental truck:
55 = 380 / time
Time = 6.91 hours
For the car:
65 = 380 / time
Time = 5.85 hours
30 minutes = 0.5 hours
If you are planning to arrive at your destination a half hour before your roommate gets there, the resting time = 6.91 - 5.85 - 0.5 = 0.56 hours
Hence, you can rest for 0.56 hours before resuming your drive and still arrive 30 minutes earlier.
Find out more on Speed at: https://brainly.com/question/4931057
