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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answer:

each class is 1.07 hours