INSTRUCTOR WITH SPI MAKES TURN AND CLB TO AVOID OVERTAKING ACFT ON INITIAL CLBOUT.

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MY STUDENT AND I HAD BEEN CLRED BY DAY TWR FOR THE OPTION TO RWY 24L; BUT THAT CLRNC WAS LATER CHANGED TO A FULL STOP ONLY DUE TO THE DEP OF VERY SLOW MOVING TFC JUST PRIOR TO OUR ARR. THE CTLR WOULD CALL OUR TKOF ROLL. THE TKOF CLRNC REQUESTED THAT WE MAINTAIN VISUAL TFC SEPARATION WITH THE SLOWER ACFT AND TURN TO A HDG OF 300 DEGS TOWARD THE USUAL PRACTICE AREA. ON TKOF; THE STUDENT SEEMED TO BE CLOSING ON THE SLOWER ACFT WHO APPEARED TO BE AT APPROX 200 FT AGL ON THE RWY HDG. TO MAINTAIN SEPARATION; I HAD THE STUDENT TURN R TO 300 DEGS AND HASTEN THE CLB. THIS SHOULD HAVE CAUSED US TO BE NO FACTOR FOR THE SLOWER ACFT AND WOULD HAVE BEEN CONSISTENT WITH THE RIGHT-OF-WAY RULES MANDATING THAT THE ACFT BEING OVERTAKEN HAS THE RIGHT-OF-WAY AND THE OVERTAKING ACFT MUST ALTER COURSE TO THE R TO PASS WELL CLR. THE PROB WAS THAT WE LOST SIGHT OF THE SLOWER ACFT DURING OUR CLBING R TURN. IF THE SIT WERE REPEATED; I WOULD IMMEDIATELY NOTIFY TWR OF LOSING VISUAL WITH THE TFC AND REQUEST A RADAR VECTOR FOR SEPARATION SINCE RADAR APCH/DEP SVC IS AVAILABLE AT DAY AND THE TWR IS EQUIPPED WITH RADAR DISPLAYS.