A motorist on a road trip drives a car at different constant speeds over several legs of the trip. He drives for 55.0 min at 55.0 km/h, 20.0 min at 60.0 km/h, and 35.0 min at 55.0 km/h and spends 30.0 min eating lunch and buying gas.
(a)
What is the total distance traveled over the entire trip (in km)?
km
(b)
What is the average speed for the entire trip (in km/h)?
km/h
To find the total distance traveled over the entire trip, we need to calculate the distance traveled during each leg and then add them up.
The distance traveled during the first leg of the trip, when driving at 55.0 km/h for 55.0 minutes, can be calculated using the formula:
Distance = Speed * Time
Substituting the values:
Distance1 = 55.0 km/h * (55.0/60) h
Similarly, we can calculate the distance traveled during the second leg, when driving at 60.0 km/h for 20.0 minutes:
Distance2 = 60.0 km/h * (20.0/60) h
Finally, we can calculate the distance traveled during the third leg, when driving at 55.0 km/h for 35.0 minutes:
Distance3 = 55.0 km/h * (35.0/60) h
Now, we can find the total distance traveled by adding the distances:
Total Distance = Distance1 + Distance2 + Distance3
To find the average speed for the entire trip, we divide the total distance by the total time taken, excluding the time spent eating lunch and buying gas.
Total Time = 55.0 min + 20.0 min + 35.0 min
Average Speed = Total Distance / Total Time
Now we can perform these calculations to find the answers.