Clocks!

MI3 wrote:Q. A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 15 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)?
A. 5:00
B. 5:34
C. 5:42
D. 6:00
E. 6:24

Answer I obtained was D, am I correct?

Thanks,
M

Let's determine the time displayed on each clock after an actual hour (60 minutes) has passed.

Clock 1 loses 15 minutes every hour. So after 60 minutes have passed, clock 1 displays the passing of 60-15 = 45 minutes.

Clock 2 gains 15 minutes for every 60 minutes displayed on clock 1. Thus, the time displayed on clock 2 is 75/60 = 5/4 the time displayed on clock 1. So after 60 minutes have passed, clock 2 displays the passing of (5/4 * 45) minutes.

Clock 3 loses 20 minutes for every 60 minutes displayed on clock 2. Thus, the time displayed on clock 3 is 40/60 = 2/3 the time displayed on clock 2. So after 60 minutes have passed, clock 3 displays the passing of (2/3 * 5/4 * 45) minutes.

Clock 4 gains 20 minutes for every 60 minutes displayed on clock 3. Thus, the time displayed on clock 4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, clock 4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.

Thus, clock 4 loses 10 minutes every hour.
In 6 hours, clock 4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, clock 4 will show a time of 6-1 = 5pm.

The correct answer is A.

Thank you Mitch, I guess I overread the problem and got lost in the "word traps".. Thanks for the explanation. As always, very helpful.