a car travels first half distance between two places with average speed of 30 km per hour and remaining half with a speed of 50 km per hour what is the average speed of the car is A 37.5KM/hr B 10km/hr //c// 42km/hr D 40km/hr
let the distance be 200km
then
100km=30km/hr*t1 or t1=10/3 hr
and
100km=50km/hr*t2 or t2=2hr
avg speed= 200km/(16/3hr)=600/16=choice A
d/2 = 30 t1 so t1 = d/60
d/2 = 50 t2 so t2 = d/100
t = t1 + t2
d = v (t1+t2) = v (d/60 + d/100)
100 = v ( 5/3 + 3/3) = (8/3) v
v = 300/8 = 37.5 km/hr
To find the average speed of the car, we need to calculate the total distance traveled and the total time taken.
Let's assume the total distance between the two places is 'd'.
The first half of the distance is traveled at an average speed of 30 km/hr. Therefore, the time taken to cover the first half is d/30.
The remaining half of the distance is traveled at an average speed of 50 km/hr. Thus, the time taken to cover the remaining half is also d/50.
The total time taken to cover the entire distance is the sum of the times taken for each half distance: (d/30) + (d/50).
Now, to calculate the average speed, we use the formula:
Average Speed = Total Distance / Total Time
The total distance is equal to 'd', and the total time is (d/30) + (d/50).
Average Speed = d / ((d/30) + (d/50))
Simplifying this expression, we get:
Average Speed = (50d + 30d) / (3d + 5d)
Average Speed = 80d / 8d
Average Speed = 10 km/hr
Therefore, the average speed of the car is 10 km/hr, which is option B.