In the second hour, the number of towels given out is 50 x 1.20 = <<50*1.20=60>>60.

In the third hour, the number of towels given out is 60 x 1.25 = <<60*1.25=75>>75.

In the fourth hour, one-third of the guests of the third hour is 75 / 3 = <<75/3=25>>25.

In the fourth hour, the number of towels given out is 75 + 25 = <<75+25=100>>100.

In total, including the first hour guests, they need to wash this many towels: 50 + 60 + 75 + 100 = <<50+60+75+100=285>>285.

# Answer

285
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
At the gym, every day, there are 300 towels laid out for guest use.  Each guest is given 1 towel during their visit.  The gym is open from 10:00 a.m. to 2:00 p.m. In the first hour, 50 guests enter the gym.  In the second hour, 20% more guests enter than during the first hour.  In the third hour, 25% more guests enter than in the second hour.  In the fourth hour, one third more guests enter than in the third hour.  In total, how many towels do they need to wash that evening?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
285
At the gym, every day, there are 300 towels laid out for guest use.  Each guest is given 1 towel during their visit.  The gym is open from 10:00 a.m. to 2:00 p.m. In the first hour, 50 guests enter the gym.  In the second hour, 20% more guests enter than during the first hour.  In the third hour, 25% more guests enter than in the second hour.  In the fourth hour, one third more guests enter than in the third hour.  In total, how many towels do they need to wash that evening?
train