Select the correct answerTwo 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?Options20102530
Question
Select the correct answerTwo 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?Options20102530
Solution 1
To solve this problem, we need to understand that the second car started an hour later than the first car but arrived at the same time. This means the second car must have been faster.
- Let's assume the distance both cars travelled is D (it can be any value, it doesn't matter for this problem because both cars travel the same distance).
- Let's say the speed of the first car is V1 and the speed of the second car is V2.
- The first car travelled for at least 6 hours. So, D = V1 * 6.
- The second car started an hour later, so it travelled for at least 5 hours. So, D = V2 * 5.
- From the above two equations, we can say that V1 * 6 = V2 * 5.
- Solving for V2, we get V2 = 1.2 * V1. This means the speed of the second car is 20% more than the speed of the first car.
So, the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is 20%.
Solution 2
To solve this problem, we need to understand that the second car started an hour later than the first car but still arrived at the same time. This means the second car must have been faster.
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Let's assume the distance both cars travelled is D (it's the same for both cars as per the problem statement).
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Let's denote the speed of the first car as S1 and the speed of the second car as S2.
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Since the first car travelled for at least 6 hours, we can say that D = S1 * 6.
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The second car started an hour later, so it travelled for 5 hours to cover the same distance. Therefore, D = S2 * 5.
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From these two equations, we can say that S1 * 6 = S2 * 5.
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Solving for S2 (the speed of the second car), we get S2 = 1.2 * S1.
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This means the speed of the second car is 20% greater than the speed of the first car.
So, the correct answer is 20.
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