To determine how much time it would take the student to run 10 km, given different speeds for the first and second halves, we can break the problem down into two parts:

1. First 5 km:

   • Speed = 10 km/h
   • Distance = 5 km

   Time for the first 5 km is calculated using the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ So, the time taken for the first 5 km is: $\text{Time}_1 = \frac{5 \, \text{km}}{10 \, \text{km/h}} = 0.5 \, \text{hours} = 30 \, \text{minutes}$

2. Second 5 km:

   • Speed = 8 km/h
   • Distance = 5 km

   Time for the second 5 km is: $\text{Time}_2 = \frac{5 \, \text{km}}{8 \, \text{km/h}} = 0.625 \, \text{hours} = 37.5 \, \text{minutes}$

3. Total time: To find the total time for the entire 10 km run, we simply add the times for each segment: $\text{Total Time} = 0.5 \, \text{hours} + 0.625 \, \text{hours} = 1.125 \, \text{hours}$

   Converting 1.125 hours to minutes: $1.125 \times 60 = 67.5 \, \text{minutes}$

Thus, the student will take 67.5 minutes to run 10 km.

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. What would happen if the student ran the entire distance at the same speed?
2. How would the total time change if the student slowed down to 6 km/h for the second half?
3. If the student wanted to finish the 10 km in exactly 1 hour, what should the speed for the second half be?
4. What is the student's average speed for the entire 10 km?
5. How long would it take to complete a 15 km run if the speeds were the same as given?

Tip: The average speed for a journey with different speeds can be found using the harmonic mean formula if the distances are the same.