A non stop bus goes from one station to another at a speed of 54 km/h. The bus returns from the second station to first station at a speed of 36 km/h. Find the average speed of the bus.
To find the average speed of the bus, we need to add the distances traveled in each of the 2 legs of the journey and divide it by the total time taken.
Let's assume that the distance between the two stations is 'd' kilometers.
In the first leg - the bus travels from the first station to the second station at a speed of 54 km/h. So, the time taken for this leg is given by:
Time taken for first leg = distance/speed = d/54
In the second leg - the bus returns from the second station to the first station at a speed of 36 km/h. So, the time taken for this leg is given by:
Time taken for second leg = distance/speed = d/36
The total time taken for the round trip is the sum of the times taken for each leg:
Total time = d/54 + d/36
Now, to find the average speed, we can use the formula:
Average speed = total distance/total time
Since the total distance is 2d (since the bus is traveling from the first station to the second, and then back to the first station), and the total time is d/54 + d/36, we can calculate the average speed:
Average speed = 2d / (d/54 + d/36)
We can simplify this expression:
Average speed = 2 / (1/54 + 1/36)
= 2 / [(36 + 54)/(36*54)]
= 2 / (90/1944)
= 3888/90
= 43.2 km/h
Therefore, the average speed of the bus is 43.2 km/h.
figure the time it took going, and coming.
t=d/v where d is the distance each way.
then
add the times
avgvelocity=2d/total time