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Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is
- a)20
- b)30
- c)25
- d)10
Correct answer is option 'A'. Can you explain this answer?
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Two cars travel the same distance starting at 10:00 am and 11:00 am, ...
Let the speed of cars be a and b and the distance =d
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Minimum time taken by 1st car = 6 hours,
For maximum difference in time taken by both of them, car 1 has to start at 10:00 AM and car 2 has to start at 11:00 AM.
Hence, car 2 will take 5 hours.
Hence a= d/6 and b = d/5
Hence the speed of car 2 will exceed the speed of car 1 by (d/5 – d/6)/d/6X 100
= (d/30 / d/6) x 100 = 20
Most Upvoted Answer
Two cars travel the same distance starting at 10:00 am and 11:00 am, ...
To find the highest possible value of the percentage by which the speed of the second car could exceed that of the first car, we need to consider the worst-case scenario where the first car travels for the longest possible time and the second car travels for the shortest possible time.
Let's assume the speed of the first car is x km/h and the speed of the second car is y km/h. We also know that the first car traveled for at least 6 hours.
Let's consider the following scenarios:
1. The first car traveled for exactly 6 hours:
In this scenario, the second car would have traveled for 5 hours. The distance traveled by both cars would be the same, as they reach their destination at the same time. Therefore, the speed of the second car can be calculated as (distance traveled by both cars) / (time traveled by the second car) = (distance traveled by the first car) / (6 hours). So, the speed of the second car will be (x/6) km/h.
2. The first car traveled for more than 6 hours:
In this scenario, the second car would have traveled for less than 5 hours. The distance traveled by both cars would still be the same. Therefore, the speed of the second car would be higher than (x/6) km/h.
So, the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is when the first car travels for exactly 6 hours. In this case, the speed of the second car would be (x/6) km/h.
To find the percentage, we can calculate:
Percentage = ((Speed of the second car - Speed of the first car) / Speed of the first car) * 100
= (((x/6) - x) / x) * 100
= ((-5x/6) / x) * 100
= -500/6
= -83.33%
Since the percentage cannot be negative, the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is 83.33%. However, we need to find the highest possible positive value.
Therefore, the answer is 83.33%, which is approximately 83%. However, none of the given options match this answer. So, there might be an error in the options provided.
Let's assume the speed of the first car is x km/h and the speed of the second car is y km/h. We also know that the first car traveled for at least 6 hours.
Let's consider the following scenarios:
1. The first car traveled for exactly 6 hours:
In this scenario, the second car would have traveled for 5 hours. The distance traveled by both cars would be the same, as they reach their destination at the same time. Therefore, the speed of the second car can be calculated as (distance traveled by both cars) / (time traveled by the second car) = (distance traveled by the first car) / (6 hours). So, the speed of the second car will be (x/6) km/h.
2. The first car traveled for more than 6 hours:
In this scenario, the second car would have traveled for less than 5 hours. The distance traveled by both cars would still be the same. Therefore, the speed of the second car would be higher than (x/6) km/h.
So, the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is when the first car travels for exactly 6 hours. In this case, the speed of the second car would be (x/6) km/h.
To find the percentage, we can calculate:
Percentage = ((Speed of the second car - Speed of the first car) / Speed of the first car) * 100
= (((x/6) - x) / x) * 100
= ((-5x/6) / x) * 100
= -500/6
= -83.33%
Since the percentage cannot be negative, the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is 83.33%. However, we need to find the highest possible positive value.
Therefore, the answer is 83.33%, which is approximately 83%. However, none of the given options match this answer. So, there might be an error in the options provided.
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