One analog clock loses 3 minutes every 2 hours and another analog clock gains 3 minutes every 4 hours. At noon, the owner sets the correct time on both clocks and leaves on a business trip. When he returns home in less than two weeks, the clocks show the same time. What time does he return? What time do the clocks show?

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12 noon

Step-by-step explanation:

Clock 1 loses 3 minutes every 2 hours. Now, 2 hours = 120 minutes.

This means, it has speed of 120 - 3 = 117 minutes for every 2 hours.

Thus, in 1 hours, it's speed = 117/2 = 58.5 min/hr

Clock 2 gains 3 minutes every 4 hours

Which means in an hour, it gains ; 4/3 minutes

Thus, it's speed an hour is; 60 + 4/3 = 61.333 min/hr

Now, When he returns home in less than two weeks, the clocks show the same time.

let's say the number of hours he was away is x. For the 2 clocks to show the same time, it means they have to show it by 12 noon at another day since it was at noon that he set the correct times before leaving.

Thus, they will both be showing 12 noon.

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