A person takes a trip, driving with a constant speed of 96.5 km/h, except for a 22.0-min rest stop. If the person's average speed is 72.4 km/h, find the following.
(a) How much time is spent on the trip?
h
(b) How far does the person travel?
km
To find the time spent on the trip, we need to use the formula:
Time = Distance / Speed
The average speed is given as 72.4 km/h, so we can set up the equation:
72.4 = Total Distance / Total Time
To find the total distance, we can use the formula:
Total Distance = (Driving Speed x Driving Time) + Rest Stop Distance
The rest stop duration is given as 22.0 min, which needs to be converted to hours:
Rest Stop Time (in hours) = 22.0 min / 60
Now, let's calculate the driving and rest stop times:
Driving Time = Total Time - Rest Stop Time
We know that the driving speed is 96.5 km/h, so we can use the equation:
Driving Time = Distance / Driving Speed
Now we have all the necessary values to solve the problem.
(a) To find the time spent on the trip:
1. Calculate the Rest Stop Time (in hours) = 22.0 min / 60 = 0.367 hours
2. Solve for Driving Time: Driving Time = Distance / 96.5 km/h
3. Solve for Total Time: Total Time = Driving Time + Rest Stop Time
(b) To find the distance traveled:
1. Substitute the given average speed and solved Total Time into the formula:
72.4 km/h = Total Distance / Total Time
2. Solve for Total Distance by multiplying both sides of the equation by Total Time.
Let's calculate the answers now.