Animals can adapt their reward expectancy to changes in delays to reward availability. When temporal relations are altered, associative models of interval timing predict that the original time memory is lost due to the updating of the underlying associative weights, whereas the representational models render the preservation of the original time memory (as previously demonstrated in the extinction of conditioned fear). The current study presents the critical test of these theoretical accounts by training mice with two different intervals in a consecutive fashion (short → long or long → short) and then testing timing behaviors during extinction where neither temporal relation is in effect. Mice that were trained with the long interval first clustered their anticipatory responses around the average of two intervals (indirect higher-order manifestation of two memories in the form of temporal averaging), whereas mice trained with the short interval first clustered their responses either around the short or long interval (direct manifestation of memory representations by their independent indexing). We assert that the original memory representation formed during training with the long interval "metrically affords" the integration of subsequent experiences with a shorter interval, allowing their co-activation during extinction. The original memory representation formed during training with the short interval would not metrically afford such integration and thus result in the formation of a new (mutually exclusive) time memory representation, which does not afford their co-activation during extinction. Our results provide strong support for the representational account of interval timing. We provide a new theoretical account of these findings based on the "metric affordances" of the original memory representation formed during training with the original intervals.