On a river, C is the mid-point between two points A and B on the same bank of…

Concept: On a river, travelling a given distance with the current (downstream) and travelling the same distance against the current (upstream) take different times, because the current adds to the boat's speed in one direction and subtracts from it in the other -- so whichever direction takes LESS time for the same distance is the downstream (with-current) direction. When one distance is a known multiple of another distance covered at the same one-way speed, the two one-way times are in that same multiple.

Application:

1. The one-way time from A to B (the full distance in this direction) is given as 20 h 20 min.

2. Since C is the midpoint of AB, the distance A to C is half of AB, so at the same one-way speed the A-to-C time is half of 20 h 20 min, i.e. 10 h 10 min.

3. The round trip A to C and back to A takes 14 h in total, so the return leg, C to A, takes 14 h minus 10 h 10 min = 3 h 50 min -- since this is faster than the outward A-to-C leg for the same distance, C-to-A (and therefore B-to-A) is the downstream direction, while A-to-C (and A-to-B) is the upstream direction.

4. Because B is twice as far from A as C is, the B-to-A time (same downstream speed, double the distance) is twice the C-to-A time: 2 x 3 h 50 min = 7 h 40 min.

Cross-check: Convert to minutes and check the upstream:downstream speed ratio is used consistently. A-to-C upstream time = 610 min for distance d; C-to-A downstream time = 230 min for the same distance d. For the full distance 2d, upstream time = 2 x 610 = 1220 min = 20 h 20 min, matching the given A-to-B time; downstream time = 2 x 230 = 460 min = 7 h 40 min, confirming the B-to-A time.

So the time to travel from B to A is 7 h 40 min.