a car moves from A to B with a constant speed of 60 kilometre per hour and returns back to its initial point with a constant speed of 40 kilometre per hour find the average speed of the car for its complete journey
Answers
Let us assume that the distance covered by the car is 'd'.
Case 1)
A car moves from A to B with a constant speed of 60 km/hr.
Here, distance covered by the car is 'd' km and speed of the car is 60 km/hr.
Distance = Speed × time
d = 60 × t1
d/60 = t1 ........(1st equation)
Case 2)
Car returns back to its initial point with a constant speed of 40 km/hr.
Now,
Distance = Speed × Time
d = 40 × t2
d/40 = t2 ..........(2nd equation)
Total distance covered by the car = Distance covered by the car from A to B and from B to A.
Since, the car follows the same pathway. So, distance covered in both cases is 'd'.
Total distance covered = d + d = 2d km
Total time taken by the car = t1 + t2
= d/60 + d/40
= (2d + 3d)/120
= 5d/120
= d/24
Average speed is defined as the ratio of total distance covered with respect to the total time taken.
i.e. Average speed = (Total distance covered)/(Total time taken)
= 2d/(d/24)
= 48 km/hr
Therefore, the average speed of the car is 48 km/hr.
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