The problem is the following:
Points A, B, C and D are in a line in the given order. A pedestrian moves out of point A to point D. Upon reaching point D he turns back and reaches point B, spending a total of 5 hours in the trip. He has spent 3 hours moving between points A and C. The distances between points A and B, B and C, C and D make up a geometric progression. The pedestrian's walking speed is 5km/h. Find the distance between points B and C
So far I've made the following progress:
- Points B-> $^b$1, C -> $^b$2, D -> $^b$3
- Marking $^b$1 as x
- The distance between A and C is $3*5=15$ km ->
- $^b2 = 15$;
- $xq=15$;
- $x=15/q$;
- $q=15/x$
- The first walk distance (A -> D, D -> B) is $15q+(xq^2-x)$
After this moment I've tried numerous options but could not get a proper outcome. Anyone willing to give a hand?