To find Stanley's average speed, we need to calculate the total distance he traveled and the total time he took.
The distance he traveled south is 120 km and he traveled at a speed of 60 km/hr. Therefore, the time taken to travel 120 km is:
time = distance / speed = 120 km / 60 km/hr = 2 hours
The distance he traveled east is 150 km and he traveled at a speed of 50 km/hr. Therefore, the time taken to travel 150 km is:
time = distance / speed = 150 km / 50 km/hr = 3 hours
The total distance traveled is 120 km + 150 km = 270 km, and the total time taken is 2 hours + 3 hours = 5 hours.
Therefore, the average speed is:
average speed = total distance / total time = 270 km / 5 hours = 54 km/hr
To find Stanley's average velocity, we need to calculate the displacement and the total time taken.
The displacement is the straight-line distance between his starting point and ending point. If we draw a diagram, we can see that Stanley traveled 120 km south and 150 km east. Therefore, the displacement is the hypotenuse of a right-angled triangle with legs of length 120 km and 150 km:
displacement = sqrt(120^2 + 150^2) = 189.7 km
The displacement is to the southeast direction.
The total time taken is 5 hours, as we calculated earlier.
Therefore, the average velocity is:
average velocity = displacement / total time = 189.7 km / 5 hours = 37.94 km/hr southeast