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Two friends, A and B, start walking simultaneously from two points, P and Q, towards points Q and P, respectively. After they reach Q and P, they again start walking back towards points P and Q. They keep on walking between points P and Q without stopping anywhere. The respective ratio of the speeds of A and B is 3 : 2.
which are 100 m apart,
Q. What is the total distance travelled by A by the time A and B meet each other at point P for the first time?
- a)100 m
- b)140 m
- c)800 m
- d)120 m
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two friends, A and B, start walking simultaneously from two points, P ...
B reaches P for the first time after he walks 100 m.
And for the second time after he walks 300 m.
And for the third time after he walks 500 m.
In all the cases, during the time in which B walks 100 m to reach point P, A will walk 3/2 × 100 m = 150 m.
3/2 × 300 m = 450 m
3/2 × 500 m = 750 m, which is not a multiple of 100.
So, A and B never meet each other at P.
Hence, answer option D is correct.
Community Answer
Two friends, A and B, start walking simultaneously from two points, P ...
Problem Analysis:
Let's assume the speed of A is 3x m/s and the speed of B is 2x m/s. We are given that the distance between P and Q is 100m.
When A and B start walking simultaneously from P and Q, they will meet at some point between P and Q. Let's assume they meet at a distance of y meters from P. At this point, the distance covered by A is y meters and the distance covered by B is (100-y) meters.
After they meet, they start walking back towards their respective starting points. The time taken by A and B to reach P and Q respectively will be the same as the time taken by them to meet at the first point.
So, the distance covered by A while going back from the meeting point to P will be equal to the distance covered by B while going back from the meeting point to Q.
Let's say this distance is z meters.
The total distance traveled by A will be the sum of the distances covered by A while going from P to the meeting point, and from the meeting point to P while going back.
Solution:
Let's solve this problem step by step:
Step 1: Find the distance covered by A and B when they meet for the first time.
- The time taken by A to cover y meters is y/3x seconds.
- The time taken by B to cover (100-y) meters is (100-y)/2x seconds.
Since they both start simultaneously, these times should be equal.
y/3x = (100-y)/2x
Simplifying this equation, we get:
2y = 300 - 3y
5y = 300
y = 60
So, A and B meet for the first time at a distance of 60 meters from P.
Step 2: Find the distance covered by A while going back to P from the meeting point.
The distance covered by A while going back to P will be equal to the distance covered by B while going back to Q.
Let's say this distance is z meters.
Step 3: Find the value of z.
- The time taken by A to cover z meters is z/3x seconds.
- The time taken by B to cover z meters is z/2x seconds.
Since they both start simultaneously, these times should be equal.
z/3x = z/2x
Simplifying this equation, we get:
2z = 3z
z = 0
So, the distance covered by A while going back to P is 0 meters.
Step 4: Find the total distance traveled by A.
The total distance traveled by A is the sum of the distances covered by A while going from P to the meeting point (y = 60 meters), and from the meeting point to P while going back (z = 0 meters).
Total distance traveled by A = y + z = 60 + 0 = 60 meters.
Therefore, the correct answer is option D - They never meet at point P.
Let's assume the speed of A is 3x m/s and the speed of B is 2x m/s. We are given that the distance between P and Q is 100m.
When A and B start walking simultaneously from P and Q, they will meet at some point between P and Q. Let's assume they meet at a distance of y meters from P. At this point, the distance covered by A is y meters and the distance covered by B is (100-y) meters.
After they meet, they start walking back towards their respective starting points. The time taken by A and B to reach P and Q respectively will be the same as the time taken by them to meet at the first point.
So, the distance covered by A while going back from the meeting point to P will be equal to the distance covered by B while going back from the meeting point to Q.
Let's say this distance is z meters.
The total distance traveled by A will be the sum of the distances covered by A while going from P to the meeting point, and from the meeting point to P while going back.
Solution:
Let's solve this problem step by step:
Step 1: Find the distance covered by A and B when they meet for the first time.
- The time taken by A to cover y meters is y/3x seconds.
- The time taken by B to cover (100-y) meters is (100-y)/2x seconds.
Since they both start simultaneously, these times should be equal.
y/3x = (100-y)/2x
Simplifying this equation, we get:
2y = 300 - 3y
5y = 300
y = 60
So, A and B meet for the first time at a distance of 60 meters from P.
Step 2: Find the distance covered by A while going back to P from the meeting point.
The distance covered by A while going back to P will be equal to the distance covered by B while going back to Q.
Let's say this distance is z meters.
Step 3: Find the value of z.
- The time taken by A to cover z meters is z/3x seconds.
- The time taken by B to cover z meters is z/2x seconds.
Since they both start simultaneously, these times should be equal.
z/3x = z/2x
Simplifying this equation, we get:
2z = 3z
z = 0
So, the distance covered by A while going back to P is 0 meters.
Step 4: Find the total distance traveled by A.
The total distance traveled by A is the sum of the distances covered by A while going from P to the meeting point (y = 60 meters), and from the meeting point to P while going back (z = 0 meters).
Total distance traveled by A = y + z = 60 + 0 = 60 meters.
Therefore, the correct answer is option D - They never meet at point P.
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Two friends, A and B, start walking simultaneously from two points, P and Q,which are 100 m apart,towards points Q and P, respectively. After they reach Q and P, they again start walking back towards points P and Q. They keep on walking between points P and Q without stopping anywhere. The respective ratio of the speeds of A and B is 3 : 2.Q. What is the total distance travelled by A by the time A and B meet each other at point P for the first time?a)100 mb)140 mc)800 md)120 mCorrect answer is option 'D'. Can you explain this answer?
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