Question 824554: A and B set out simultaneously to meet each other from two places 165 km apart. A travels 15 km the first day, 14 km the second, 13 km the third and so on. While B travels 10 km the first day, 12 km the second, 14 km the third and so on. When will they meet? 4 days 8 days 6 days 10 days
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A and B set out simultaneously to meet each other from two places 165 km apart.
A travels 15 km the first day, 14 km the second, 13 km the third and so on.
While B travels 10 km the first day, 12 km the second, 14 km the third and so on.
When will they meet? 4 days 8 days 6 days 10 days.
:
I can't seem to find an equation to solve this, the brute force method:
When they meet they will have traveled a total of 165 mi
Find the total Each day. 6 days is the winner
Day Adist Bdist
1 15 10
2 14 12
3 13 14
4 12 16
5 11 18
6 10 20
------------
total 65 + 90 = 165 mi
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A and B set out simultaneously to meet each other from two places 165 km apart. A travels 15 km the first day, 14 km the second, 13 km the third and so on. While B travels 10 km the first day, 12 km the second, 14 km the third and so on. When will they meet? 4 days 8 days 6 days 10 days
A’s total distance traveled represents an arithmetic progression
Formula for the sum of an AP:  , with:
 : the sum of the distances that A will travel to meeting point
 : the 1st distance traveled by A, or 15
 : the common difference for A, or - 1
This results in the following equation for total distance A will travel to meeting point: 
B’s total distance traveled represents an arithmetic progression
Formula for the sum of an AP:  , with:
 : the sum of the distances that B will travel to meeting point
: the 1st distance traveled by B, or 10
: the common difference for B, or 2
This results in the following equation for total distance B will travel to meeting point: 
Now, the sum of the distances traveled by A, plus the sum of the distances traveled by B, equals total
distance between them, OR
 ------- Multiplying by LCD, 2
(n - 6)(n + 55) = 0
n, or number of days it’ll take for them to meet =  OR n = - 55 (ignore)
You can do the check!!
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