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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