Two Clocks
Two faulty analog clocks are set correctly at midnight, one that gains a
x
number of minutes (under 50 minutes) every hour, and one that loses a
y
number of minutes (under 50 minutes) every hour. At 6:00 PM (real time) the same day, they will both read the same time. The next time the clock that gains minutes "thinks" it is midnight, the other clock will read "1:20". Find
.
The answer is 110.
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1 solution
After 16 hours (12:00 AM to 6:00 PM), the clocks differ by 12 hours. This means that the ratio of x + y to 60 (minutes to hours conversion) is equal to 16 to 24.
x + y = 40 minutes.
Now, when the fast clock thinks it is midnight, it thinks 24 hours have passed. But the other clock thinks it is 1:20 PM. The difference between 1:20 PM and midnight is 10 hours 40 minutes = 640 minutes.
640 minutes ÷ ( x + y ) = 16 hours that actually passed.
In 16 hours, the fast clock gained 8 hours, meaning that in 1 hour, the fast clock gains 30 minutes.
x = 3 0
y = 1 0
3 x + 2 y = 9 0 + 2 0 = 1 1 0