Brain Teasers
Crossing Paths
A person starts off walking in a perfectly straight line at uniform speed. After a mile, a second person starts walking at uniform speed from the same starting point and catches up with the first guy after another mile. At this time, the second person turns at an angle of 60 degrees west. They both continue walking in straight lines for a certain period of time. Then, the second person turns 60 degrees east. They both continue in straight lines. Will the second person cross the first's path in front, behind or at the same time?
Answer
They will intercept!Person 2 catches up with the first guy after another mile
This tells us that person 2 is walking twice the speed of 1.
He goes off at an angle of 60 degrees, but his speed in the same direction as the first person is 2cos60
cos60 is 1/2 so the speed in the same direction is the same.
When he turns, his speed is 2sin60 = 1!
It doesn't matter when he turns, the paths will eventually meet up again!
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Comments
Very good!
I don't think so. As you say, they are walking parallel to each other, with the second person some distance to the first person's left. Their paths will not cross, since parallel lines do not cross.
sorry, but I agree with rab, = never cross. if we are missing soemthing and we are wrong, please explain.
Actually "the second person turns 60 degrees west" is the confusing part. If it is read as 60 degrees from the original direction, the teaser works.
Rab and dumbell, the problem is with the explanation of the answer, not the answer itself. They aren't walking parallel, they're walking along the same line to begin with. From above, it would almost look like a big, straightlined P.
There are many things wrong with this teaser. Firstly, the question asks whether he will cross in front, behind or at the same place. This is not answered!
Secondly, it is a Mathematical teaser and despite the confusing explanation, since when does 2sin60 = 1? Actually, 2sin60 = 2xroot(3)/2 = 1.732 approx.
I think Krishnan is correct. If the person turned 120 degrees or 60 degrees towards the East from the ORIGINAL direction, the the vector component in the original direction would be 2cos60 = 1 so what the teaser is attempting to say is that both persons continue in the original direction at the same speed. Thus they will cross paths at teh same time (they will meet again).
Whew! This teaser is in a category of its own - one where you have to make up the question as well as find the answer!
Secondly, it is a Mathematical teaser and despite the confusing explanation, since when does 2sin60 = 1? Actually, 2sin60 = 2xroot(3)/2 = 1.732 approx.
I think Krishnan is correct. If the person turned 120 degrees or 60 degrees towards the East from the ORIGINAL direction, the the vector component in the original direction would be 2cos60 = 1 so what the teaser is attempting to say is that both persons continue in the original direction at the same speed. Thus they will cross paths at teh same time (they will meet again).
Whew! This teaser is in a category of its own - one where you have to make up the question as well as find the answer!
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