Speed-Distance-Time: Calculate Total Time for 24km Multi-Speed Run

Daniel runs on the field along the following path:

How long does it take Daniel to finish the run?

To solve this problem, we'll apply the formula for time to each segment of Daniel's run and sum the results.

• Step 1: Calculate the time for the first segment.
  The formula for time is $t = \frac{d}{v}$.
  For the first segment: $d = 7 \, \text{km}$, $v = 8 \, \text{km/h}$.
  Thus, the time is $t_1 = \frac{7}{8} \approx 0.875 \, \text{hours}$.
• Step 2: Calculate the time for the second segment.
  For the second segment: $d = 4 \, \text{km}$, $v = 9 \, \text{km/h}$.
  Thus, the time is $t_2 = \frac{4}{9} \approx 0.444 \, \text{hours}$.
• Step 3: Calculate the time for the third segment.
  For the third segment: $d = 13 \, \text{km}$, $v = 7 \, \text{km/h}$.
  Thus, the time is $t_3 = \frac{13}{7} \approx 1.857 \, \text{hours}$.
• Step 4: Sum the times from all segments to get the total time.
  Total time $T = t_1 + t_2 + t_3 \approx 0.875 + 0.444 + 1.857 = 3.176 \, \text{hours}$.

Rounding this to one decimal place provides $T \approx 3.2$ hours.

Therefore, the solution to the problem is $3.2 \, \text{hours}$.