To find out how fast the train must travel for the next 100 km to achieve an average speed of 70 km/h for the entire journey, we first need to understand how average speed is calculated.
The average speed is given by the formula:
Average Speed = Total Distance / Total Time
Let’s assume the total distance of the journey is 200 km, with the first segment being 100 km. We want the average speed to be 70 km/h.
First, we find the total time required to travel 200 km at an average speed of 70 km/h:
Total Time = Total Distance / Average Speed
Total Time = 200 km / 70 km/h = 2.857 hours (approximately)
Now, let’s denote the time taken to travel the first 100 km as t1, and the speed for the first segment can be considered as s1. The time taken for the first leg is:
t1 = 100 km / s1
This leads us to the rest of the journey: the time taken to travel the next 100 km, represented as t2, will be:
t2 = Total Time – t1 = 2.857 hours – (100 km / s1)
For the average speed to equal 70 km/h, we need:
t2 = 100 km / s2
where s2 is the speed for the next 100 km. Therefore, we equate the two expressions for time:
100/s2 = 2.857 – (100/s1)
From this equation, you can rearrange it to express the relationship between s1 and s2. However, without knowing the speed for the first segment, we can’t calculate an exact speed for s2 without further information on the first leg of the journey. If we assume that s1 is equal to the desired average speed of 70 km/h for simplification:
t1 = 100 km / 70 km/h = 1.42857 hours
Plugging this back into our equation gives:
t2 = 2.857 – 1.42857 = 1.42843 hours
And to find s2:
s2 = 100 km / t2 = 100 km / 1.42843 hours ≈ 70.0 km/h
Thus, if the train travels at an average speed of 70 km/h for the first 100 km, it must continue at the same speed for the second leg to maintain that average. If the speed in the first leg is less than 70 km/h, the required speed for the next leg must increase to make up for it.