# Average speed.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?

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A person runs 100 meters at 15 m/s, 400 meters at 10 m/s and 800 meters at 8m/s. To determine the average speed, find the total distance that the person runs and the total time taken to do the same.

Use the formula t = d/s

To run the 100 m at 15 m/s, the time required is 100/15

To run the 400 m at 10 m/s, the time required is 400/10 = 40

To run 800 m at 8 m/s, the time required is 800/8 = 100 s

The total distance run by the person is 100 + 400 + 800 = 1300 m. The total time taken for this is 100/15 + 40 + 100 = 440/3

The average speed is 1300/(440/3) = 195/22 m/s

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