Final answer:
To find the average speed of the whole journey, you calculate the time taken for each part using the distance covered and the speed at which it was traveled, then sum these times to find the total time. The average speed is the total distance of the journey divided by this total time.
Step-by-step explanation:
To calculate the average speed for the whole journey where different parts are covered at different speeds, we need to use the formula for average speed which is the total distance traveled divided by the total time taken.
Let 'D' be the distance of the whole journey. Then:
- 1/3 of the journey is covered at 25 km/h
- 1/4 of the journey is covered at 30 km/h
- The rest of the journey is covered at 50 km/h
For the first part of the journey:
Distance = D/3
Speed = 25 km/h
Time = Distance/Speed = (D/3) / 25
For the second part of the journey:
Distance = D/4
Speed = 30 km/h
Time = Distance/Speed = (D/4) / 30
For the remaining part of the journey, which is (1 - 1/3 - 1/4) of D, we know that:
Distance = D - (D/3 + D/4) = D/12
Speed = 50 km/h
Time = Distance/Speed = (D/12) / 50
The total time for the journey is the sum of the times for each part:
Total Time = (D/3)/25 + (D/4)/30 + (D/12)/50
The total distance is the sum of all parts which is D:
Total Distance = D
Therefore, the average speed for the entire journey is:
Average Speed = Total Distance / Total Time
Once you calculate the above expression using the provided speeds, you will have the average speed of the journey. Remember to verify that the result is reasonable and makes sense given the speeds involved in the different parts of the journey.