If a person runs 100 meters at 15 m/s, 400 meters at 10 m/s and 800 meters at 8m/s , what is the average speed?

The formula of average speed is the ratio between
the total distance covered and the time needed for covering the total
distance.

To total distance covered could be calculated.
We have to determine the time needed to cover entire
distance.

Total distance = 100 + 400 + 800 =
1300m

We'll use the rule of 3 to determine the time for
each distance covered:

 15m.......................1
s

100m.......................x
s

We'll cross multiply:

15x =
100

x1 = 100/15 s

The time
needed for covering 100m is t1 = 6.6 s

The time needed for
covering 400 m is t2 = 40 s

 The time needed for covering
800 m is t3 = 100 s

The entire time for covering 1300m
is:

T = t1+t2+t3

T = 6.6 + 40
+ 100

T = 146.6
s

We'll determine the average speed for
covering the distance of 1300
m:

av. speed =
1300/146.6

av. speed = 8.86
m/s