A woman drives a car from one city to another with different constant speeds along the trip. She drives at a speed of 50.0 km/h for 20.0 min, 85.0 km/h for 25.0 min, makes a stop for 30.0 min, then continues at 45.0 km/h for 35.0 min, at which point she reaches her destination.
(a) What is the total distance between her starting point and destination (in km)?
(b) What is the average speed for the entire trip (in units of km/h)?
To find the total distance traveled by the woman, we need to calculate the distance traveled during each leg of her trip and then sum them up.
Let's break down the trip into different segments:
Segment 1:
Speed = 50.0 km/h
Time = 20.0 min = 20.0/60 = 1/3 hour (converted to hours)
Distance1 = speed * time
Distance1 = 50.0 km/h * (1/3) hour
Segment 2:
Speed = 85.0 km/h
Time = 25.0 min = 25.0/60 = 5/12 hour (converted to hours)
Distance2 = speed * time
Distance2 = 85.0 km/h * (5/12) hour
Segment 3:
The woman makes a stop for 30.0 min = 30.0/60 = 1/2 hour (converted to hours). During this time, the car is not moving, so the distance traveled is 0 km.
Segment 4:
Speed = 45.0 km/h
Time = 35.0 min = 35.0/60 = 7/12 hour (converted to hours)
Distance4 = speed * time
Distance4 = 45.0 km/h * (7/12) hour
Now we can calculate the total distance:
Total distance = Distance1 + Distance2 + Distance4
To find the average speed, we'll calculate the total time taken for the entire trip:
Total time = Time1 + Time2 + Time3 + Time4
Total time = (1/3) hour + (5/12) hour + 0 hour + (7/12) hour
Finally, the average speed is given by:
Average speed = Total distance / Total time
Now let's plug in the values and calculate the answers:
Distance1 = 50.0 km/h * (1/3) hour = 16.67 km
Distance2 = 85.0 km/h * (5/12) hour = 35.42 km
Distance4 = 45.0 km/h * (7/12) hour = 26.25 km
Total distance = 16.67 km + 35.42 km + 0 km + 26.25 km
Total distance = 78.34 km
Total time = (1/3) hour + (5/12) hour + 0 hour + (7/12) hour
Total time = 1.08333 hour
Average speed = 78.34 km / 1.08333 hour
Therefore, the answers are:
(a) The total distance between her starting point and destination is 78.34 km.
(b) The average speed for the entire trip is approximately 72.25 km/h.