A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 10 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
Choose the most appropriate option: A) 5:00 B) 5:34 C) 5:42 D) 6:00 E) 6:24
C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15= 
<gadget id="calculator">60-15</gadget>
<output>45</output>
45 minutes have passed.   C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60= 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.   C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.   C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of  4/3 * 2/3 * 5/4 * 45= 
<gadget id="calculator"> 4/3 * 2/3 * 5/4 * 45</gadget>
<output>50</output>
50 minutes.   C4 loses 10 minutes every hour.   In 6 hours, C4 will lose   6*10= 
<gadget id="calculator">  6*10</gadget>
<output>60</output>
60 minutes= 1 hour.   Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6pm.   The correct answer is 6:00.
<result>D</result>
A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 10 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?