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 --- total time in school: y = 7 + 3/5 y = 35/5 + 3/5 y = 38/5 y = 2*(38/5) y = 76/10 --- lunch time: z = 1/2 z = 5*(1/2) z = 5/10 --- time switching classes: w = 7/10 --- 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 --- 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 --- answer: each class is 1.07 hours
