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If two person A and B start at the same time in opposite direction from two points and after passing each other they complete the journey in a and b hours respectively, then the ratio of A’s and B’s speed will be:
- a)√a : √b
- b)√b: √a
- c)√a + √b: √a - √b
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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If two person A and B start at the same time in opposite direction fr...
Let total distance be D km. and A's speed be x km/hr and B's speed be y km/hr
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If two person A and B start at the same time in opposite direction fr...
Understanding the Problem
When two persons A and B start from two points and move towards each other, they meet at a certain point. After meeting, they take different times to complete their respective journeys. The goal is to find the ratio of their speeds.
Key Variables
- Let the speed of A be represented as vA.
- Let the speed of B be represented as vB.
- The time taken by A to reach the destination after they meet is 'a' hours.
- The time taken by B to reach the destination after they meet is 'b' hours.
Distance Relationships
- After meeting, A travels a distance of vA * a.
- After meeting, B travels a distance of vB * b.
Since they started from two points and met, the distances they cover after meeting must be equal to the total distance they initially covered until they met.
Setting Up the Equation
From the point they met, we can express the distances:
- Distance covered by A after meeting: vA * a
- Distance covered by B after meeting: vB * b
Since they met at the same time from their respective starting points, we equate the distances:
vA * a = vB * b
Finding the Speed Ratio
To find the ratio of speeds, we rearrange the equation:
vA/vB = b/a
Taking the square roots to find the ratio of speeds:
√(vA/vB) = √(b/a)
Thus, we obtain:
vA/vB = √b : √a
Conclusion
The ratio of A's speed to B's speed is:
vA : vB = √b : √a
Therefore, the correct answer is option 'B', which represents the ratio as √b : √a.
When two persons A and B start from two points and move towards each other, they meet at a certain point. After meeting, they take different times to complete their respective journeys. The goal is to find the ratio of their speeds.
Key Variables
- Let the speed of A be represented as vA.
- Let the speed of B be represented as vB.
- The time taken by A to reach the destination after they meet is 'a' hours.
- The time taken by B to reach the destination after they meet is 'b' hours.
Distance Relationships
- After meeting, A travels a distance of vA * a.
- After meeting, B travels a distance of vB * b.
Since they started from two points and met, the distances they cover after meeting must be equal to the total distance they initially covered until they met.
Setting Up the Equation
From the point they met, we can express the distances:
- Distance covered by A after meeting: vA * a
- Distance covered by B after meeting: vB * b
Since they met at the same time from their respective starting points, we equate the distances:
vA * a = vB * b
Finding the Speed Ratio
To find the ratio of speeds, we rearrange the equation:
vA/vB = b/a
Taking the square roots to find the ratio of speeds:
√(vA/vB) = √(b/a)
Thus, we obtain:
vA/vB = √b : √a
Conclusion
The ratio of A's speed to B's speed is:
vA : vB = √b : √a
Therefore, the correct answer is option 'B', which represents the ratio as √b : √a.
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If two person A and B start at the same time in opposite direction from two points and after passing each other they complete the journey in a and b hours respectively, then the ratio of A’s and B’s speed will be:a)√a : √bb)√b: √ac)√a + √b: √a - √bd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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