Veritas Prep
Three friends, A, B and C have houses along a straight road, in that order. If all three want to meet up at one of their houses, what is the minimum combined distance they need to travel?
1) The distance between A's house and B's house is 2 miles
2) The distance between A's house and C's house is 8 miles
OA B
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Three friends, A, B and C have houses along a straight road, in that order. If all three want to meet...
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Since B's house lies between A's and C's, this is the only possible picture that we can draw:
A <--- 2 ---> B <--- 6 ---> C
The minimum combined distance that the 3 friends have to travel will be in the case when they meet at B's house, in which case, A will travel 2 miles, and C will travel 6 miles, and B will travel 0 miles, for a total of 8 miles.
If we select any other house as final destination, the combined distance would be more (If A final : 10, if C final: 14) because in both the other case, two of the friends will have to travel same parts of the road. In other words, one friend will have to in effect pick up other friend from its house and then proceed to third friend's house.
Answer: 8
A <--- 2 ---> B <--- 6 ---> C
The minimum combined distance that the 3 friends have to travel will be in the case when they meet at B's house, in which case, A will travel 2 miles, and C will travel 6 miles, and B will travel 0 miles, for a total of 8 miles.
If we select any other house as final destination, the combined distance would be more (If A final : 10, if C final: 14) because in both the other case, two of the friends will have to travel same parts of the road. In other words, one friend will have to in effect pick up other friend from its house and then proceed to third friend's house.
Answer: 8
