t option to
ping sets the time-to-live field in the packet, this has nothing to do with how many pings are sent or for what duration. IIRC the IPV4 TTL field typically limits the number of routers the packet may traverse (max "hops").
You should probably use
ping -c count -i interval for example
ping -c 240 -i 60 would send one ping every 60 seconds for four hours.
This probably isn't a good use of ping. The manual says
This program is intended for use in network testing, measurement and management.
Because of the load it can impose on the network it is unwise to use ping
during normal operations or from automated scripts.