A person takes a trip, driving with a constant speed of 92.5 km/h except for a 20.0 min rest stop. If the person's average speed is 71.2 km/h, how much time is spent on the trip and how far does the person travel?
average speed=distance/time
71.2=(92.5*Timedriving)/(timedriving+1/3)
solve for time driving, then add 20 min for the total time (or 1/3 hour)
how far? 92.5*timedriving
To find the time spent on the trip, we can use the formula:
Time = Distance / Speed
Let's assume the total distance traveled is represented by "d" km, and the time spent on rest stop is 20.0 min (or 20/60 = 1/3 hour). We can also use the equation:
Average Speed = Total Distance / Total Time
Substituting the given values:
71.2 km/h = d km / (Total Time - 1/3 hour)
Now we need to find the Total Time.
To find the distance traveled, we can use the formula:
Distance = Speed × Time
Since the person drove at a constant speed of 92.5 km/h, except for the rest stop, we can break down the trip into two parts:
1. Distance before the rest stop: s1 = 92.5 km/h × (Total Time - 1/3 hour)
2. Distance during the rest stop: s2 = 0 km (since the person is not moving during the rest stop)
Therefore, the total distance traveled is:
d = s1 + s2 = 92.5 km/h × (Total Time - 1/3 hour) + 0 km
Now we can substitute this value into the equation for average speed:
71.2 km/h = (92.5 km/h × (Total Time - 1/3 hour)) / (Total Time - 1/3 hour)
To solve for Total Time, we can multiply through by (Total Time - 1/3 hour):
71.2 km/h × (Total Time - 1/3 hour) = 92.5 km/h × (Total Time - 1/3 hour)
Now we can simplify and solve for Total Time:
71.2 km/h × Total Time - 71.2 km/h × (1/3 hour) = 92.5 km/h × Total Time - 92.5 km/h × (1/3 hour)
Simplifying further:
22.5 km/h × Total Time = 21.3 km/h × (1/3 hour)
Now divide both sides by 22.5 km/h:
Total Time = (21.3 km/h × (1/3 hour)) / 22.5 km/h
Calculating this expression:
Total Time = (21.3 × (1/3)) / 22.5 hour
Total Time = 0.71 hour
To find the distance traveled, we can substitute Total Time back into the equation:
d = 92.5 km/h × (Total Time - 1/3 hour)
d = 92.5 km/h × (0.71 hour - 1/3 hour)
d = 92.5 km/h × (0.38 hour)
Calculating this expression:
d = 35.15 km
Therefore, the time spent on the trip is approximately 0.71 hour (or 42.6 minutes) and the person travels a distance of approximately 35.15 km.