Average velocity and average speed

When a particle has moved from position x_{i} to
position x_{f} during the time interval Dt =
t_{f} - t_{i}, its average velocity
v_{avg }is

v_{avg } is a vector; it has a
direction and a magnitude.

The average speed S_{avg}^{
}is

S_{avg}^{ }does not have a direction. It
only has a magnitude and it is always positive. S_{avg }is an example of
a scalar quantity.

x versus t graph

Average velocity is the slope of the straight line connecting the initial and final points on the x(t) curve.

Question:

A particle moving on a straight line takes Dt_{1}
= 100 sec to move from x_{1} = 5.0 m to x_{2} = 20. m and it
takes Dt_{2} = 150 sec to move back to
position x_{3}=- 5.0 m. What is the particle average velocity and
average speed during its total journey?

Answer: