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

Question

Daniel runs on the field along the following path:

7 km8 km/h4 km9 km/h13 km7 km/h

How long does it take Daniel to finish the run?

Video Solution

Step-by-Step Solution

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=dv t = \frac{d}{v} .
    For the first segment: d=7km d = 7 \, \text{km} , v=8km/h v = 8 \, \text{km/h} .
    Thus, the time is t1=780.875hours t_1 = \frac{7}{8} \approx 0.875 \, \text{hours} .
  • Step 2: Calculate the time for the second segment.
    For the second segment: d=4km d = 4 \, \text{km} , v=9km/h v = 9 \, \text{km/h} .
    Thus, the time is t2=490.444hours t_2 = \frac{4}{9} \approx 0.444 \, \text{hours} .
  • Step 3: Calculate the time for the third segment.
    For the third segment: d=13km d = 13 \, \text{km} , v=7km/h v = 7 \, \text{km/h} .
    Thus, the time is t3=1371.857hours 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=t1+t2+t30.875+0.444+1.857=3.176hours 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 T3.2 T \approx 3.2 hours.

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

Answer

3.2 hours