Randi ran two laps around a 400m track.She completed the first lap in 50seconds and then decreased her speed by 5% for the second lap.
Find:
A)her speed on the first lap
B)her speed on the second lap
C)her total time for the two laps
D)her average speed for the two laps
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To find the necessary values, we can follow these steps:
A) To find Randi's speed on the first lap, we can use the formula rate = distance/time. Since Randi ran one lap around a 400m track in 50 seconds, her speed for the first lap is:
Speed = Distance / Time
Speed = 400m / 50s
Speed = 8m/s
Therefore, Randi's speed on the first lap is 8 meters per second (m/s).
B) To find Randi's speed on the second lap, we need to take into account the 5% decrease in speed. We can calculate the decrease by multiplying the speed of the first lap by 0.05 (5% as a decimal), and subtracting it from the speed of the first lap. So, her speed on the second lap is:
Speed of the second lap = Speed of the first lap - (Speed of the first lap * Decrease)
Speed of the second lap = 8m/s - (8m/s * 0.05)
Speed of the second lap = 8m/s - 0.4m/s
Speed of the second lap = 7.6m/s
Therefore, Randi's speed on the second lap is 7.6 meters per second (m/s).
C) To find Randi's total time for the two laps, we need to add up the time it took for each lap. Since she completed the first lap in 50 seconds and the second lap at a steady speed, her total time for the two laps is:
Total Time = Time for the first lap + Time for the second lap
Total Time = 50s + 50s
Total Time = 100s
Therefore, Randi's total time for the two laps is 100 seconds (s).
D) To find Randi's average speed for the two laps, we can use the formula average speed = total distance / total time. Since she ran two laps around a 400m track and her total time is 100 seconds, her average speed is:
Average Speed = Total Distance / Total Time
Average Speed = (2 laps * 400m) / 100s
Average Speed = 800m / 100s
Average Speed = 8m/s
Therefore, Randi's average speed for the two laps is 8 meters per second (m/s).
To find the answers to these questions, let's break down the given information step by step:
A) To find Randi's speed on the first lap, we need to know the distance covered in that lap and the time taken. Since she completed one lap on a 400m track, her speed on the first lap can be calculated by dividing the distance by the time.
Speed = Distance / Time
Speed = 400m / 50s
Speed = 8 m/s
Therefore, Randi's speed on the first lap is 8 m/s.
B) To find Randi's speed on the second lap, we are told that she decreased her speed by 5% from the first lap. We can calculate her reduced speed by subtracting 5% of her original speed from the first lap speed.
Reduced Speed = First Lap Speed - (5% of First Lap Speed)
Reduced Speed = 8 m/s - (0.05 * 8 m/s)
Reduced Speed = 8 m/s - 0.4 m/s
Reduced Speed = 7.6 m/s
Therefore, Randi's speed on the second lap is 7.6 m/s.
C) To find Randi's total time for the two laps, we need to add the time taken for the first lap (50 seconds) and the time taken for the second lap. Since we know the distance covered (400m) and the speed on the second lap (7.6 m/s), we can use the formula:
Time = Distance / Speed
Time(second lap) = 400m / 7.6 m/s
Time(second lap) = 52.63 seconds (rounded to two decimal places)
Total Time = Time(first lap) + Time(second lap)
Total Time = 50 seconds + 52.63 seconds
Total Time = 102.63 seconds
Therefore, Randi's total time for the two laps is 102.63 seconds.
D) To find Randi's average speed for the two laps, we need to use the formula:
Average Speed = Total Distance / Total Time
Total Distance = 2 laps * 400m/lap
Total Distance = 800m
Average Speed = 800m / 102.63 s
Average Speed ≈ 7.79 m/s (rounded to two decimal places)
Therefore, Randi's average speed for the two laps is approximately 7.79 m/s.
A. distance = 400 m; time = 50 seconds
distance = rate x time. Solve for rate.
B. distance = 400 m
time for second lap is 50s-0.05(50s) = ?
solve for rate.
C. total time = time for first lap + time for second lap = ?
D. average speed (rate) = total distance/total time.