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