Hi,
By default PI will wait for 1 min for synchronous response .If it doesn't receive within that time period it will throw timeout exception.
From your description "request message reached to target system" means url configured by you is correct and target system is up and running.
Check the below.
Check with target system folks how much time they are taking to respond back
Check with n/w and firewall teams for any failures in traffic b/w PI and target system by sharing time period.They can check and confirm you on this .
Regards
Venkat