15/45= 1/3 (hours) =20 (minutes)

At this time, B left.

5* 1/3=5/3 (km)

The rest of the journey is equal to the opposite direction of the teacher and B.

Let the time be x.

X*(5+45)= 15-5/3

X=4/ 15 (hours) = 16 (minutes)

Then the teacher went back (with B)

Time is still 16 minutes.

Total 20+ 16+ 16 = 52 minutes.