If it takes Hugo twice the amount of time to fold a medium box than a small box, then he needs 2*3 = <<6=6>>6 seconds for the medium box

If Tom can fold either the small or medium box in 4 seconds, then he's faster at folding the medium box than Hugo because 4s < 6s

If Hugo can fold the small box in 3 seconds, then he's faster at folding the small boxes than Tom because 3s < 4s

Therefore Hugo should fold all small boxes and Tom should fold all the medium ones before doing the other size where they are slower

If there are 2400 small boxes and Hugo can fold 1 box in 3 seconds, then it would take him 2400*3 = <<2400*3=7200>>7200 seconds to fold all boxes

If there are 1800 medium boxes and Tom can fold 1 box in 4 seconds, then it would take him 1800*4 = <<1800*4=7200>>7200 seconds to fold all medium boxes

Given that they need the same amount of time to fold all boxes, and are doing it simultaneously they will need 7200 seconds to fold all the boxes

# Answer

7200
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Hugo can fold a small box in 3 seconds and a medium one in twice that time. Tom can fold both the small and medium boxes in 4 seconds. If Hugo and Tom want to leave as early as possible, how long (in seconds) will it take them to fold 2400 small boxes and 1800 medium boxes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7200
Hugo can fold a small box in 3 seconds and a medium one in twice that time. Tom can fold both the small and medium boxes in 4 seconds. If Hugo and Tom want to leave as early as possible, how long (in seconds) will it take them to fold 2400 small boxes and 1800 medium boxes?
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