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A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds is
- a)1 : 2
- b)4 : 1
- c)1 : 4
- d)2 : 1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A certain distance is covered at a certain speed. If half of this dist...
We know that Speed = Distance/Time
Case 1:
Let 100 kms be covered in 1 hour
Hence, speed = 100 kmph
Let 100 kms be covered in 1 hour
Hence, speed = 100 kmph
Case 2:
Distance = 100/2 = 50 km
Time = 2 hours
Speed = 50/2 = 25 kmph
Required ratio = 100 kmph : 25 kmph
= 4 : 1
Distance = 100/2 = 50 km
Time = 2 hours
Speed = 50/2 = 25 kmph
Required ratio = 100 kmph : 25 kmph
= 4 : 1
Most Upvoted Answer
A certain distance is covered at a certain speed. If half of this dist...
Understanding the Problem
We are given a distance that is covered at a certain speed. Let's denote the total distance as D and the speed for the first part as S. The time taken to cover the entire distance D can be expressed as:
- Time = Distance / Speed = D / S
Now, we need to analyze the second part where half of the distance is covered at double the time.
Key Details of the Second Scenario
- Distance covered = D / 2 (half of the total distance)
- Time taken = 2 * (D / S) = 2D / S (double the time taken to cover the total distance)
Now, we can determine the speed for the second part:
Calculating the Second Speed
- Speed for the second part = Distance / Time
- Speed = (D / 2) / (2D / S) = (D / 2) * (S / 2D) = S / 4
Finding the Ratio of Speeds
Now, we have two speeds:
1. The first speed: S
2. The second speed: S / 4
To find the ratio of the two speeds:
- Ratio = Speed 1 : Speed 2 = S : (S / 4) = S : S/4
This simplifies to:
- Ratio = 4 : 1
Conclusion
Thus, the ratio of the two speeds is 4:1, confirming that the correct answer is option 'B'.
We are given a distance that is covered at a certain speed. Let's denote the total distance as D and the speed for the first part as S. The time taken to cover the entire distance D can be expressed as:
- Time = Distance / Speed = D / S
Now, we need to analyze the second part where half of the distance is covered at double the time.
Key Details of the Second Scenario
- Distance covered = D / 2 (half of the total distance)
- Time taken = 2 * (D / S) = 2D / S (double the time taken to cover the total distance)
Now, we can determine the speed for the second part:
Calculating the Second Speed
- Speed for the second part = Distance / Time
- Speed = (D / 2) / (2D / S) = (D / 2) * (S / 2D) = S / 4
Finding the Ratio of Speeds
Now, we have two speeds:
1. The first speed: S
2. The second speed: S / 4
To find the ratio of the two speeds:
- Ratio = Speed 1 : Speed 2 = S : (S / 4) = S : S/4
This simplifies to:
- Ratio = 4 : 1
Conclusion
Thus, the ratio of the two speeds is 4:1, confirming that the correct answer is option 'B'.
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A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds isa)1 : 2b)4 : 1c)1 : 4d)2 : 1Correct answer is option 'B'. Can you explain this answer?
Question Description
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