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Math  /  Data & Statistics

QuestionThe Boden brothers had a 25-meter swimming race at a pool. Michael gave Hasson a 3-meter head start. Use the given data below to determine who won the race and by how many seconds.
Hasson's Swim
Michael's Swim \begin{tabular}{|c|c|} \hline Time (sec)(\mathrm{sec}) & Distance (m)(\mathrm{m}) \\ \hline 6 & 8.4 \\ \hline 8 & 11.2 \\ \hline 10 & 14 \\ \hline 12 & 16.8 \\ \hline \end{tabular} ✓\checkmark Michael won the race by about □\square seconds.

Studdy Solution

STEP 1

1. Hasson has a 3-meter head start, so his initial position is at 3 meters.
2. The race is 25 meters long.
3. We need to determine the time each swimmer takes to reach 25 meters.
4. Michael's data is given in a table, and Hasson's data is inferred from the image description.

STEP 2

1. Determine Hasson's swimming speed and calculate the time he takes to complete 25 meters.
2. Determine Michael's swimming speed and calculate the time he takes to complete 25 meters.
3. Compare the times to determine the winner and the time difference.

STEP 3

Calculate Hasson's swimming speed using the points provided in the image description. Assume the points are (6, 9.6), (8, 11.8), (10, 14), and (12, 16.2).
Calculate the speed between two points, e.g., between (6, 9.6) and (8, 11.8):
Speed=Distance DifferenceTime Difference=11.8−9.68−6=2.22=1.1 m/s\text{Speed} = \frac{\text{Distance Difference}}{\text{Time Difference}} = \frac{11.8 - 9.6}{8 - 6} = \frac{2.2}{2} = 1.1 \, \text{m/s}

STEP 4

Calculate the time for Hasson to swim 25 meters. He starts at 3 meters, so he needs to swim 22 meters.
Time=DistanceSpeed=221.1=20 seconds\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{22}{1.1} = 20 \, \text{seconds}

STEP 5

Calculate Michael's swimming speed using the given table data. Use the points (6, 8.4) and (8, 11.2):
Speed=11.2−8.48−6=2.82=1.4 m/s\text{Speed} = \frac{11.2 - 8.4}{8 - 6} = \frac{2.8}{2} = 1.4 \, \text{m/s}

STEP 6

Calculate the time for Michael to swim 25 meters:
Time=251.4≈17.86 seconds\text{Time} = \frac{25}{1.4} \approx 17.86 \, \text{seconds}

STEP 7

Compare the times:
- Hasson's time: 20 seconds - Michael's time: 17.86 seconds
Michael wins the race.
Calculate the time difference:
Time Difference=20−17.86=2.14 seconds\text{Time Difference} = 20 - 17.86 = 2.14 \, \text{seconds}
Michael won the race by about 2.14 \boxed{2.14} seconds.

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