It's pretty simple so there must be something obviously wrong with it but what is it? Starter is an electric signal emitter that sends a pulse to the laser source and the detector, starting a counter in both, it is located at the exact halfway point between them.
So basically you send out the starter signal that starts a counter clock in both ends at the same time (or does it?) then you fire the laser. When you fire the laser the counter at the source stops. When the detector detects the laser the counter there stops too. Now you have the time it took for light to get from source to detector. What is the problem?
LaserSource-----------------------------Detector
<----starter---->