Grades 1-2 Video Solutions 2023-2023_1-2

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Problem number 19. The map shows five villages, A, B, C, D, and E, and the distances in kilometers between them.  Only two villages are the same distance apart no matter which route you choose. Which are these two villages?  If two villages are the same distance apart no matter which way we choose, then each of the distances will be half of the whole road.  So first, let's find the length of the whole road. From A to B, it's 7 kilometers. From B to C, it's 2. From C to D is 6. From D to E is 4.  And from E to A, which is where we started, it's 5.  Add those together. 6 plus 4 is 10. You can add 7 and 2, which gives us 19. And 5 more gives us 24.  So the whole track, or the whole road, is 24 kilometers long. Half of that is going to be 12.  So the two villages we're looking for are 12 kilometers apart no matter which way we go.  Now, let's try to figure out which of these villages are 12 kilometers apart.  Notice that none of these roads by themselves have a length of 12. So it will be a combination of roads, and it will not be two villages that are next to each other.  It makes sense to start with A. From A to B, it's 7 kilometers. Then if we go to C, that's 9 kilometers. Still not 12. From C to D, it's an extra 6 kilometers.  9 plus 6 is 15. So we've gone too far, and also we know that none of the villages are 12 kilometers from A. We can cross off choices D and E.  So let's see if B is one of the villages. From B to C, it's 2 kilometers. From C to D, it's 6, which makes a total of 8 from B to D. And then to E, it's another 4 kilometers.  And 8 plus 4 is 12. So it is 12 kilometers from B to E. Let's just make sure that going the other direction, we also get 12.  From B to A, it's 7 plus 5 from A to E, which also makes 12. So two villages that are 12 kilometers apart are B and E.  And if you have time on the exam, you can check the other choices just to make sure you did not make mistakes.

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