When and where are two man together who are walking at different pace?

Question

A and B begin,at 6 a.m. on the same day, to walk along a road in the same direction, B having a start of 14 kilometers and each walking from 6 a.m. to 6 p.m. daily. A walks 10 kilometers, at a uniform pace, the first day, 9 the second, 8 the third, and so on. B walks 2 kilometers, at a uniform pace, the first day, 4 the second, 6 the third, and so on. When and where are they together?

Answer 1

Noon on day 3. 23 kilometers from point A.

Let me show my work:

A is at kilometer 0+10 = 10 at the end of day 1
B is at kilometer 14+2 = 16 at the end of day 1

A is at kilometer 10+9= 19 at the end of day 2
B is at kilometer 16+4= 20 at the end of day 2

This leaves A with one kilometer to make up at the beginning of day 3.

At a pace of 8 kilometers per day on day three, A has walked 4 (or half) of them by noon. At a pace of 6 kilometers per day, B has walked three (or half) by noon. This is where A catches up with B.

Take their final day 2 totals and add half of day 3's pace to each:

A. 19 + 4 = 23
B. 20 + 3 = 23

So, like I said earlier without the work. They meet 23 kilometers from point A at 12pm on day three.

They also meet at the conclusion of day 4, after their speed totals overlap. So, they actually meet twice, as pointed out below.

Answer 2

Person A-: 10 + 9 + 8 + 7 = 34 by the end of day 4

Person B-: 14km start + 2 + 4 + 6 + 8 = 34 by the end of day 4

i.e. They will both be together at 6pm on Day 4