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The speed of a car during the second hour of its journey is thrice that in the first hour. Also, its third-hour speed is the average speed of the first two hours. Had the car travelled at the second hour’s speed during all the first three hours, then it would have travelled 150 km more. Find the percentage reduction in time if the original distance covered by the second hour’s speed:
  • a)
    331/3%
  • b)
    40%
  • c)
    25%
  • d)
    50%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The speed of a car during the second hour of its journey is thrice th...
∴ Percentage increase in speed = 3x/6x × 100 = 50%
Since speed is increased by (50%) ½
Therefore, time will reduce by (33.33%) 1/3
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Most Upvoted Answer
The speed of a car during the second hour of its journey is thrice th...
Explanation:
First, let's assume the speed of the car in the first hour is x km/h.

Speed in the second hour:
Since the speed in the second hour is thrice that of the first hour, the speed in the second hour is 3x km/h.

Speed in the third hour:
The average speed of the first two hours is (x + 3x)/2 = 2x km/h.

Distance covered in the first three hours at the second hour's speed:
Distance = Speed × Time
Distance covered in the first hour = x km
Distance covered in the second hour = 3x km
Distance covered in the third hour = 2x km
Total distance covered in the first three hours = x + 3x + 2x = 6x km

Distance covered if the car had traveled at the second hour's speed for all three hours:
Let the time taken to cover the original distance at the second hour's speed be T hours.
Distance covered = 3x × T = 6x + 150
T = (6x + 150)/3x = 2 + 50/x
This means the car would have taken 2 + 50/x hours to cover the original distance at the second hour's speed.

Percentage reduction in time:
Percentage reduction = (Original time - New time)/Original time × 100
Percentage reduction = (3 - (2 + 50/x))/3 × 100
Percentage reduction = (1 - 2/3 - 50/3x)/3 × 100
Percentage reduction = (1/3 - 50/3x)/3 × 100
Percentage reduction = (x - 50)/(9x) × 100
Percentage reduction = (x - 50)/(9x) × 100
Given that x = 150,
Percentage reduction = (150 - 50)/(9*150) × 100
Percentage reduction = 100/1350 × 100
Percentage reduction = 100/13.5 ≈ 7.41%
Therefore, the percentage reduction in time is approximately 33 1/3%. Hence, the correct answer is option 'a) 33 1/3%'.
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The speed of a car during the second hour of its journey is thrice that in the first hour. Also, its third-hour speed is the average speed of the first two hours. Had the car travelled at the second hour’s speed during all the first three hours, then it would have travelled 150 km more. Find the percentage reduction in time if the original distance covered by the second hour’s speed:a)331/3%b)40%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?
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