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?

x = time per class
y = total time in school
z = lunch time
w = time switching classes
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total time in school:
y = 7 + 3/5
y = 35/5 + 3/5
y = 38/5
y = 2*(38/5)
y = 76/10
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lunch time:
z = 1/2
z = 5*(1/2)
z = 5/10
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time switching classes:
w = 7/10
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y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (76/10 - 5/10 - 7/10)/6
x = (76 - 5 - 7)/(10*6)
x = (64)/(10*6)
x = (2*2*2*2*2*2)/(2*5*2*3)
x = (2*2*2*2)/(5*3)
x = 16/15

x = 1.0666666666
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check:
y = 7 + 3/5
y = 7.6
z = 1/2
z = 0.5
w = 7/10
w = 0.7
y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (7.6 - 0.5 - 0.7)/6
x = 1.0666666666
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each class is 1.07 hours