As he was initially running at the same speed as Amy, we have to work that out, so take the distance/time (converting minutes to hours for km/hr) 4.375/(31.5 /60) = 8.33...km/hr.
As we now know how long he ran for (in the q) towards B from A and his and Amy's joint speed we can calculate the distance travelled (once again converting minutes to hours): (15.75/60) x 8.33... = 2.1875km.
We now have the distance from A when he turns around to run back and his new faster pace (13.3km/hr in the q) so do distance/speed for the time taken:
2.1875/13.3 = 0.164474 hours - x60 to convert to minutes = 9.86844 -> 9 minutes + (convert the seconds) .86844 x 60 =52.1064 seconds.
Just did this rough so possibly not exact with rounding errors but it simplifies to 9 mins 52s to the nearest second.
Good luck with the ucat!