My friend and I started simultaneously towards each other from two places 100…
2023
My friend and I started simultaneously towards each other from two places 100 m apart. After walking 30 m, my friend turned left and went 10 m, then he turned right and went 20 m, then he turned right again and came back onto the road on which he had started walking. If we both walked with the same speed, what is the distance between us at that point in time?
- A.
50 m
- B.
20 m
- C.
30 m
- D.
40 m
Show answer & explanation
Correct answer: B
Concept: When someone's path bends away from and then back onto a straight road, only the movements parallel to the road change its net progress along it; equal turns of the same length in opposite directions (for example a left turn followed later by an equivalent right-turn segment back onto the road) cancel out. Also, if two people start together and walk at the same speed for the same length of time, they cover the same total distance, whatever path each takes.
Application:
Picture the road connecting the two starting points as a single straight line; the distance between the friend's starting point and your starting point is 100 m.
The friend walks 30 m along the road, his first stretch, moving forward toward your starting point; road progress so far: 30 m.
He turns left and walks 10 m off the road, a perpendicular movement, not counted along the road.
He turns right and walks 20 m; this segment runs parallel to the road in the same forward direction, adding 20 m of road progress: 30 + 20 = 50 m so far.
He turns right again and walks back onto the same road; this final stretch is another perpendicular movement of the same 10 m, exactly cancelling the earlier sideways step.
So the friend's net position is 50 m from his own starting point along the road, and the total distance he actually walked is 30 + 10 + 20 + 10 = 70 m.
Since you both walk at the same speed for the same time, you also cover 70 m in that time; walking straight along the road toward the friend's starting point, you reach a point 70 m from your own start, which is 100 - 70 = 30 m from the friend's starting point.
The gap between you and your friend at this moment = (friend's distance from his own start) - (your distance from the friend's start) = 50 - 30 = 20 m.
Cross-check: Placing the friend's starting point at position 0 and your starting point at position 100 on this line, the friend ends at 50 and you, walking from 100 toward 0 by 70, end at 30; the same 50 - 30 = 20 m gap, confirming the answer.