Aryan has to travel certain distance from his home at a speed of 5 kilometre hours on his way back to home the speed decreases to 3 kilo metre per hour find his average speed.
since time = distance/speed,
time out = d/5
time back: d/3
avg speed = total distance / total time
= 2d/(d/5 + d/3)
= 2/(1/5 + 1/3)
= 2/(8/15)
= 15/4
Close to 4, but not quite.
From home the speed was 5km/hr. Back to home the speed was 3km/hr. Therefore his average speed=5km/hr+3km/hr devide by 2. That's 8km/hr divide by 2. So his average speed was 4km/hr.
To find the average speed, we need to calculate the total distance traveled and the total time taken.
Let's assume the distance from Aryan's home to his destination is 'd' kilometers.
On his way to the destination, Aryan traveled the entire distance at a speed of 5 kilometers per hour. The time taken for this part of the journey is given by:
Time taken = Distance / Speed = d / 5
On his way back home, Aryan traveled the same distance but at a speed of 3 kilometers per hour. The time taken for this part of the journey is given by:
Time taken = Distance / Speed = d / 3
Now, let's calculate the total time taken for the entire journey:
Total time = Time taken to go + Time taken to return
= (d / 5) + (d / 3)
To find the average speed, we divide the total distance traveled by the total time taken:
Average speed = Total distance / Total time
= 2d / ((d / 5) + (d / 3))
Simplifying the above expression, we get:
Average speed = 2 / ((1 / 5) + (1 / 3))
Now, let's calculate the average speed:
Average speed = 2 / (0.2 + 0.3333)
= 2 / 0.5333
≈ 3.75 kilometers per hour
Therefore, Aryan's average speed for the entire journey is approximately 3.75 kilometers per hour.