Problem 978

【Solution】Solution: The time taken for the first meeting is: $360 \div(80+40)=3$ (hours), at this point the motorcycle has traveled $80 \times 3=240$ (km);

Second meeting: After the meeting, the motorcycle returns to point B, traveling another 240 km, taking 3 hours.
During this time, the car travels another 120 km, leaving $240-120=120$ (km) to point B,
The motorcycle turns around from point B and heads towards the car, the time taken for the second meeting is $120 \div(40+80)=1$ (hour);
Third meeting: The motorcycle travels 80 km, after loading the medicine, the motorcycle reaches point B and travels another 80 km, the car travels 40 km,
Leaving $80-40=40$ (km) to point B, taking 1 hour;
The third meeting takes $40 \div(80+40)=\frac{1}{3}$ (hour), at the meeting, the motorcycle travels $80 \times \frac{1}{3}=\frac{80}{3}$ (km), and then travels another $\frac{80}{3}$ km, taking $\frac{80}{3} \div 80=\frac{1}{3}$ (hour).
Therefore, the motorcycle travels a total of: $240 \times 2+80 \times 2+\frac{80}{3} \times 2=693 \frac{1}{3}$ (km); the total time taken is: $3 \times 2+1 \times 2+\frac{1}{3} \times 2=8 \frac{2}{3}$ (hours).

Answer: To transport all 6 boxes of medicine to point B, it takes at least $8 \frac{2}{3}$ hours, during which the motorcycle travels a total of $693 \frac{1}{3}$ km.