If a car covers 2/5th of the total distance with V1 speed and 3/5th distance with V2, then average speed is?
To find the average speed, we need to use the formula:
Average Speed = Total Distance / Total Time
First, let's assume the total distance covered is "D" and the total time taken is "T".
According to the given information, the car covers 2/5th of the total distance (2D/5) with speed V1 and 3/5th of the total distance (3D/5) with speed V2.
The time taken to cover the 2/5th distance is (2D/5)/V1 = (2D)/(5V1).
The time taken to cover the 3/5th distance is (3D/5)/V2 = (3D)/(5V2).
Therefore, the total time taken (T) is:
T = (2D)/(5V1) + (3D)/(5V2)
To find the average speed, we need to find the total distance covered (D).
Total Distance = 2D/5 + 3D/5 = (2D + 3D)/5 = 5D/5 = D
Substituting D back into the equation for T, we have:
T = (2D)/(5V1) + (3D)/(5V2) = D/(5V1) + D/(5V2) = D(1/V1 + 1/V2)/5
Now, we can calculate the average speed using the formula:
Average Speed = Total Distance / Total Time
Average Speed = D / (D(1/V1 + 1/V2)/5) = 5 / (1/V1 + 1/V2)
Therefore, the average speed is 5 / (1/V1 + 1/V2).
To find the average speed, we need to calculate the total time taken to cover the entire distance and then divide it by the total distance.
Let's assume the total distance is D.
The distance covered with V1 speed is (2/5) * D, and the time taken for this distance is (2/5) * D / V1.
Similarly, the distance covered with V2 speed is (3/5) * D, and the time taken for this distance is (3/5) * D / V2.
Now, to find the total time taken, we add the time taken for the two parts of the journey:
Total time = (2/5) * D / V1 + (3/5) * D / V2
To find the average speed, we divide the total distance (D) by the total time:
Average speed = D / ( (2/5) * D / V1 + (3/5) * D / V2 )
Simplifying the above expression, we get:
Average speed = 1 / ( (2/5) / V1 + (3/5) / V2 )
Therefore, the average speed is 1 divided by the weighted sum of the reciprocals of the individual speeds, where the weights are the respective proportions of distance covered.
Note: Make sure to convert the fractions (2/5 and 3/5) into their decimal equivalents before performing the calculations.
avg speed= distanc/time
time for V1:
time= 2/5)/V1
time for V2:
time= 3/5/V2
total time= 2/5V1 + 3/5V2
=(2V2+3V1)/5V1V2
avgspeed=5V1V2/(2V2+3V1)