The timing characteristics of scintillators must be understood in order to determine which applications they are appropriate for. Polyethylene naphthalate (PEN) and polyethylene teraphthalate (PET) are common plastics with uncommon scintillation properties. Here, we report the timing characteristics of PEN and PET, determined by exciting them with 120 GeV protons. The test beam was provided by Fermi National Accelerator Laboratory, and the scintillators were tested at the Fermilab Test Beam Facility. PEN and PET are found to have dominant decay constants of 34.91 ns and 6.78 ns, respectively.