Add a quarter of the time until seven o'clock this evening to a fifth of the time since noon. What time is it?
by 
bluebluenic
ANSWERS: 3
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Let's say T is the time right now (in hours). If you call noon zero, then the time until 7:00 PM is 7-T. The time since noon is T by definition. So the expression is: T + (1/4)(7-T) + (1/5)T = (19/20)T + 7/4 = (0.95)T + 1.75 The time right now is 12:52 PM = 0.87 hours. The calculated time is thus (.95)(.87) + 1.75 = 2.58 hours = 2:35 PM. So...?
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Following xprofessor's answer one more step ... Suppose (1/4)(7-T) + (1/5)T = T itself. Then 5(7-T) + 4T = 20T 35 = 21T T = 1:40 pm Check: Time until seven = 5:20 One quarter of that = 1:20 Time since noon = 1:40 On fifth of that = 0:20 0:20 + 1:20 = 1:40pm
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Look at the clock!
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