Mai spends 7 3/5 hours in school each day. her lunch period is 1/2 hour long, and she spends a total of 7/10 hour switching rooms between classes. the rest of her day is spent in 6 classes that are all the same length. how long is each class?show work!

Lunch: 0.5 Changing rooms: 0.7 
7.75 - 1.2 = 6.55 
6.55 / 6 = 1.09 hours/class

7 3/5 = 38/7 hours 
1/2 hour 
7/10 hour 

convert them so they all have the same denominators 

38/7 = 380/70
1/2   = 35/70 
7/10 = 49/70 
 
add 35/70 and 49/70 then subtract from 380/70

35/70 + 49/70 = 84/70
380/70 - 84/70 = 296/70 

296/70 divided into 6 classes 

296/70 divide 6 = 296/70 x 1/6 
= 74/105 x 60 mins
= 42.28571429
each class is approximately 42 mins long