ProleFeed13 wrote:

Asifpirlo wrote:

Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?

A. 1 ≤n ≤23

B. 3 ≤n ≤21

C. 5 ≤n ≤19

D. 6 ≤n ≤18

E. 9 ≤n ≤15

Honestly, I just assumed this was all in a straight direct line away from Sam's home. So 12 + 6 -2 + 3 = 19 as the upper bound, and C is the only choice that fits this.

I did the same but on the lower limit. If you think about it, it is correct approach because, the farthest that Red Rock can exist from his home is when he ran 6 miles from grey hill in exactly opposite direction of the home. so Red Rock will be 18 miles from home. And the max of the required range will be when he runs 3 miles in the opposite direction again after he retraced 2 miles back. this gives 18-2+3 = 19 miles as upper limit.

Likewise to get lower limit of the range, Red rock must be closest to his home which is 12-6 = 6 miles. he retraces 2 miles away to 8 miles and turns around and goes back 3 miles giving distance of 5 miles from home as lower limit.

took little over 2 mins for this.

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