Question

in a relay race, four runners (a, b, c, and d) work together to run a total distance of 400 m. each runner runs 100 m before handing a baton to the next runner.

a clock starts measuring time when runner a begins. the time is recorded when each runner completes their part of the race. these times are shown on the distance vs. time graph below.

graph: y-axis (distance, m) with 0, 100, 200, 300, 400; x-axis (time, s) with 0, 20, 40, 60, 80, 100. segments: a (blue) from (0,0) to (20,100); b (red) from (20,100) to (60,200); c (orange) from (60,200) to (80,300); d (purple) from (80,300) to (90,400) (approximate, based on graph labels).

Explanation:

To determine the speed of each runner, we use the formula \( \text{speed} = \frac{\text{distance}}{\text{time}} \). Each runner runs 100 m.

Runner A:

• Distance: \( 100 \, \text{m} \)
• Time: \( 20 \, \text{s} \) (from \( t = 0 \) to \( t = 20 \))
• Speed: \( \frac{100}{20} = 5 \, \text{m/s} \)

Runner B:

• Distance: \( 100 \, \text{m} \) (from 100 m to 200 m)
• Time: \( 60 - 20 = 40 \, \text{s} \)
• Speed: \( \frac{100}{40} = 2.5 \, \text{m/s} \)

Runner C:

• Distance: \( 100 \, \text{m} \) (from 200 m to 300 m)
• Time: \( 80 - 60 = 20 \, \text{s} \)
• Speed: \( \frac{100}{20} = 5 \, \text{m/s} \)

Runner D:

• Distance: \( 100 \, \text{m} \) (from 300 m to 400 m)
• Time: \( 90 - 80 = 10 \, \text{s} \) (assuming the final time is 90 s, as the graph reaches 400 m near \( t = 90 \))
• Speed: \( \frac{100}{10} = 10 \, \text{m/s} \)

If the question was to find the fastest runner, the answer is Runner D with a speed of \( 10 \, \text{m/s} \).

(Note: Adjust the final time for D based on the exact graph; if the graph’s D point is at \( t = 90 \), this holds. If not, recalculate with the correct time difference.)

Final Answer (for fastest runner):

Runner D, with a speed of \( \boldsymbol{10 \, \text{m/s}} \) (or specify the question’s exact request, e.g., speed of D is \( 10 \, \text{m/s} \)).

Answer:

To determine the speed of each runner, we use the formula \( \text{speed} = \frac{\text{distance}}{\text{time}} \). Each runner runs 100 m.

Runner A:

• Distance: \( 100 \, \text{m} \)
• Time: \( 20 \, \text{s} \) (from \( t = 0 \) to \( t = 20 \))
• Speed: \( \frac{100}{20} = 5 \, \text{m/s} \)

Runner B:

• Distance: \( 100 \, \text{m} \) (from 100 m to 200 m)
• Time: \( 60 - 20 = 40 \, \text{s} \)
• Speed: \( \frac{100}{40} = 2.5 \, \text{m/s} \)

Runner C:

• Distance: \( 100 \, \text{m} \) (from 200 m to 300 m)
• Time: \( 80 - 60 = 20 \, \text{s} \)
• Speed: \( \frac{100}{20} = 5 \, \text{m/s} \)

Runner D:

• Distance: \( 100 \, \text{m} \) (from 300 m to 400 m)
• Time: \( 90 - 80 = 10 \, \text{s} \) (assuming the final time is 90 s, as the graph reaches 400 m near \( t = 90 \))
• Speed: \( \frac{100}{10} = 10 \, \text{m/s} \)

If the question was to find the fastest runner, the answer is Runner D with a speed of \( 10 \, \text{m/s} \).

(Note: Adjust the final time for D based on the exact graph; if the graph’s D point is at \( t = 90 \), this holds. If not, recalculate with the correct time difference.)

Final Answer (for fastest runner):

Runner D, with a speed of \( \boldsymbol{10 \, \text{m/s}} \) (or specify the question’s exact request, e.g., speed of D is \( 10 \, \text{m/s} \)).