A drive took some hours to travel from Rome to Milan. His average speed for the whole journey was 80 km/hour. For the first half of the journey he traveled at an average speed of 50km/hour.
Find his average speed for the second half of the journey. In this case half refers to half of the time.
Find his average speed for the second half of the journey. In this case half refers to half of the distance.
Let half the journey, time wise, be x hours.
Thus the full journey time is 2x hours.
Avg speed = total distance/total time
80 = total distance/2x
Thus total distance=160x km
For the first part of the journey, his distance travelled was speed x time, or 50x km
For the second part of the journey, his distance travelled was160x - 50x = 110x km.
Thus his average speed in the second part of the journey was distance/ time = 110x/x = 110 km/hr.
Use a similar strategy for part 2 of your question.
To find the average speed for the second half of the journey, we'll first need to determine the time taken for the entire journey and the time taken for the first half.
Let's assume that the total time taken for the journey is "T" hours.
Since the average speed for the entire journey is given as 80 km/hour, we can use the formula:
Total distance = Average speed × Time taken
The total distance for the journey from Rome to Milan remains the same, regardless of the speed:
Total distance = Average speed × Time taken
Total distance = 80 km/h × T hours
Now, let's find the time taken for the first half of the journey. We know that the average speed for the first half is 50 km/hour. Using the same formula:
Distance for the first half = Average speed × Time taken for the first half
Since the first half is defined as half of the time, we can represent it as T/2:
Distance for the first half = 50 km/h × (T/2) hours
Since the total distance for the journey remains the same, we can subtract the distance for the first half from the total distance to find the distance for the second half:
Distance for the second half = Total distance - Distance for the first half
Distance for the second half = 80 km/h × T hours - 50 km/h × (T/2) hours
Now that we have the distance for the second half, we can calculate the average speed for the second half by dividing the distance by the time:
Average speed for the second half = Distance for the second half ÷ Time taken for the second half
Since the time taken for the second half is T/2, we can substitute it into the formula:
Average speed for the second half = Distance for the second half ÷ (T/2) hours
Now you can plug in the expressions we found earlier for the distance of the second half to calculate the average speed.