# 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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Speed is given by the relation, speed = distance/ time. This can be written as time = distance/ speed.

Now the person runs 100 m at 15 m/s. The time required is 100/15.

The next 400 m are run at 10 m/s. The time required is 400/ 10.

The final 800 m are run at 8 m/s. The time required is 800/8.

So the total distance run is 100 + 400 + 800 = 1300.

The total time taken is 100/15 + 400/10 + 800/8

=> 20/3 + 40 + 100

=> 440/3 s.

Therefore the average speed is total distance/ total time = 1300 / (440/3)

= 195/22 m/s

= **8.86 m/s approximately**.

The time taken by the person to run 100 m at 15 m/s = 100/15 seconds.

The time taken by the person to run 400m at 10 m/s is 400/10 = 40 second.

The time taken by the person to 800m at the speed of 8 m/s = 800/8 = 100 seconds.

So the total distance run by the person = 100+400+800 =1300 meters.

The total time taken by the perso to run 1300 meters = (100/15+ 40+100) s = 146.6667 s.

Therefore the average speed of the person = total distance covered/total time taken = 1300m/146.6667 = 8.86m/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**