A person takes a trip, driving with a constant speed of 93.5 km/h except for a 22.0 min rest stop. If the person's average speed is 68.0 km/h, how much time is spent on the trip and how far does the person travel?
h
km
time take=80.67min
distance=91.42km
kjkjb
To find the time spent on the trip and the distance traveled, we can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the total time spent on the trip first.
Given:
Constant speed = 93.5 km/h
Rest stop time = 22.0 min = 22.0/60 hours = 0.367 hours
Average speed = 68.0 km/h
To calculate the total time spent on the trip, we need to subtract the rest stop time from the total time:
Total Time = Driving Time + Rest Stop Time
Let's calculate the driving time first:
Driving Time = Total Time - Rest Stop Time
Now, we can use the formula to find the Total Time:
Average Speed = Total Distance / Total Time
68.0 km/h = Total Distance / Total Time
The constant speed will only be applicable during the driving time, so we can write:
Total Distance = Constant Speed * Driving Time
Substituting the driving time equation into the total distance equation:
68.0 km/h = (Constant Speed * Driving Time) / Total Time
Rearranging the formula to solve for Total Time:
Total Time = (Constant Speed * Driving Time) / Average Speed
Now we can substitute in the values we already know:
Total Time = (93.5 km/h * Driving Time) / 68.0 km/h
To solve for the driving time, we'll rearrange the formula:
Driving Time = (Total Time * Average Speed) / Constant Speed
Substituting the values:
Driving Time = (Total Time * 68.0 km/h) / 93.5 km/h
Now, we can substitute this value back into the total distance equation:
Total Distance = Constant Speed * Driving Time
Total Distance = 93.5 km/h * [(Total Time * 68.0 km/h) / 93.5 km/h]
Now we can calculate the values:
Driving Time = (Total Time * 68.0 km/h) / 93.5 km/h
Total Time = (93.5 km/h * Driving Time) / 68.0 km/h
Total Distance = 93.5 km/h * [(Total Time * 68.0 km/h) / 93.5 km/h]
After substituting the values, we will have the time spent on the trip and the distance traveled.