# a motor car covers 1/3 part of total distance with v1=10km/hr second 1/3 part with v2=20 km/hr and rest 1/3 part v3=60km/hr. what is the average speed of the car?

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The formula for average speed is:

`s_(ave)= ( t o tal distance)/( t o tal time)`

The given in the above problem are:

`v_1 = 10` km/hr `v_2=20` km/hr `v_3= 60` km/hr

`d_1 = 1/3x` `d_2= 1/3x ` `d_3=1/3x `

where x represents the total distance covered by the car.

Total distance `= d_1+d_2+d_3 = x`

Then, determine time taken for each distance covered using the formula speed = d/t.

`t_1 = d_1/v_1 = (1/3x)/10 = 1/30x`

`t_2 = d_2/v_2 = (1/3x)/20 = 1/60x`

`t_3= d_3/v_3 = (1/3x)/60 = 1/180x`

Determine the total time taken to travel the x distance.

Total time `= t_1+t_2+t_3= 1/30x + 1/60x+1/180x = 6/180x+3/180x+1/180x`

Total time `= 10/180x= 1/18x`

Then substitute *total distance=x* and *total time =*`1/18x` to the formula of average speed.

`s_(ave)= x/(1/18x) = 1/(1/18) = 18` ``

**Hence, average speed is 18 km/hr.**

Lets say total distance travelled by the car is S. For each 1/3 of distances we assume that the time consumed was t1,t2 and t3 respectively.

We know that distance traveled = velocity * time

Then

S/3 = v1*t1 = 10*t1------> t1 = S/30

S/3 = v2*t2 = 20*t2------> t2 = S/60

S/3 = v3*t3 = 60*t3------> t3 = S/180

So average speed of car = Total distance/total time

= S/(t1+T2+t3)

= S/(S/30+S/60+S/180)

= S/(S(1/30+1/60+1/180))

= 1/(1/30+1/60+1/180)

= 18

**So the average speed of the car is 18km/h.**