We simulated a method for measuring quantum tunnelling time using the adiabatic theorem. This method causes backaction in a different way from the conventional method using the Larmor clock. Especially, we focused on the numerical simulation of the dynamics of a wave packet, rather than a single plane wave, since the latter extends over all of space and the concept of tunneling times for the wave is unclear. By comparing the outcomes of these two types of measurements, we showed that the quantum tunneling time may appear shorter for higher barriers due to the limits on the precision of tunneling time measurements, which are caused by the energy of the clock.