1999 sunfire se coolant leaks after about 5/10 running, temp gauge shoots up

have only had the car for about a week. while running an errand that was only a few
miles away the car overheated and after getting home the coolant was gone. let it sit
for a while and replaced coolant and started, after 5/10 minutes it got hot and temp
went up. i could see the coolant coming out somewhere around the passenger side by
where i put the coolant in. it had the serpintine belt all wet..... is this possibly a hose
problem or maybe a gasket thing. any help would be good. thank you