A man travels distance 18km/h from his house to an exhibition by rickshaw at km/h and return back on cycle at 20km/h find his average speed for the whole journey
To find the average speed for the whole journey, we need to consider the total distance traveled and the total time taken.
Let's assume the distance from the man's house to the exhibition is "d" km.
First, let's calculate the time it took to travel from his house to the exhibition by rickshaw.
Time taken = distance / speed
Time taken by rickshaw = d / r km/h
Next, let's calculate the time it took to return back from the exhibition on a cycle.
Time taken by cycle = d / c km/h
Now, let's calculate the total time taken for the whole journey.
Total time taken = Time taken by rickshaw + Time taken by cycle
Total time taken = (d / r) + (d / c) hours
Finally, let's calculate the average speed for the whole journey.
Average speed = total distance / total time taken
Average speed = 2d / [(d / r) + (d / c)] km/h
Therefore, the average speed for the whole journey is 2d / [(d / r) + (d / c)] km/h.
To find the average speed for the entire journey, we need to calculate the total distance traveled divided by the total time taken.
Let's break down the journey into two parts: the journey from the house to the exhibition, and the journey back from the exhibition to the house.
1. Journey from house to exhibition by rickshaw:
Given:
Speed of the rickshaw = x km/h
Distance = 18 km
To calculate the time taken for this part of the journey, we use the formula:
Time = Distance / Speed
Time taken for this part of the journey = 18 / x hours
2. Journey back from the exhibition to the house on a cycle:
Given:
Speed of the cycle = 20 km/h
Distance = 18 km
To calculate the time taken for this part of the journey, we use the same formula:
Time = Distance / Speed
Time taken for this part of the journey = 18 / 20 hours
Now, to find the total time for the entire journey, we add the times for the two parts:
Total time taken = (18 / x) + (18 / 20) hours
Finally, to calculate the average speed, we divide the total distance by the total time:
Average speed = Total distance / Total time
Total distance = Distance + Distance = 18 km + 18 km = 36 km
Average speed = 36 / [(18 / x) + (18 / 20)] km/h
So, the average speed for the whole journey is 36 / [(18 / x) + (18 / 20)] km/h.
please proofread.
time outward = d / 18
time back = d/20
total time = d/18 + d/20
total distance = 2 d
av speed = 2 d/ [d/18 + d/20]
= 2/(1/18 +1/20)
= 2/(.056+.05) = 2/.106
= 18.9 km/h