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18 Sep 2018, 21:54
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John begins running due north from point P1 at a speed of 2 meters per second, while Peter starts running due south at the same moment from another point, P2 , at the same speed. What is the distance between Peter and John 5 seconds later?
(1) Point P1 is 10 meters due east of point P2.
(2) Peter is 40 meters due north of John after 10 seconds.
(1) Point P1 is 10 meters due east of point P2.
(2) Peter is 40 meters due north of John after 10 seconds.
[Any suggestions why (2) is not enough? It suggests that both are on the same ax N-S and run toward each other.] solved
21 Sep 2018, 09:23
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St 1: Distance between P1 and P2 on the straight line is given as 10m.
Now John traveled North up to point R. P1R = 10m.
Peter traveled same distance south. Name the point as S. P2S= 10m.
Join the points R&S and name the point as O where this line intersects line P1P2. We have two similar right angle triangles OP2S & OP1R.
P2S/P1R=OP2/OP1=OS/OR=1. OS and OR can be calculated easily and OS+OR = Distance between John and Peter. Sufficient.
St 2: After 10 seconds they will be separated by 40 meters as John traveled 20 m north and peter traveled 20m south but the distance between them varies as per the distance between points P1 and P2. Not Sufficient.
Answer:A
Now John traveled North up to point R. P1R = 10m.
Peter traveled same distance south. Name the point as S. P2S= 10m.
Join the points R&S and name the point as O where this line intersects line P1P2. We have two similar right angle triangles OP2S & OP1R.
P2S/P1R=OP2/OP1=OS/OR=1. OS and OR can be calculated easily and OS+OR = Distance between John and Peter. Sufficient.
St 2: After 10 seconds they will be separated by 40 meters as John traveled 20 m north and peter traveled 20m south but the distance between them varies as per the distance between points P1 and P2. Not Sufficient.
Answer:A
