[subject] + 赶紧 / 赶快 + [verb phrase]
赶紧 and 赶快 go before a verb and say the action should happen right now, because there's no time to lose. Both are spoken.
As a command, with or without 吧, they mean "hurry up and …".
Both also describe how someone reacted to a situation: they did something at once. 赶紧 is the more common of the two in this kind of report.
赶紧 and 赶快 are adverbs: they go before the verb and can't describe how fast someone does something. For speed, use 快 or a 得 phrase.