Clock word problem. 4. On planet X, their clocks have only 9 hours, and each hour contains 63minutes. Determine all the times (up to two decimal places) when the handsof a clock on planet X have both hands pointing in exactly the same direction.

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In planet X, the clock would be calibrated from 1 to 9 with intervals of 7, since there is only 9 hours per clock cycle and one hour is 63 minutes. 

Starting from 9 and reaching back to 9, the minute hand and the hour hand of the clock will...

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In planet X, the clock would be calibrated from 1 to 9 with intervals of 7, since there is only 9 hours per clock cycle and one hour is 63 minutes. 

Starting from 9 and reaching back to 9, the minute hand and the hour hand of the clock will point in the same direction for 9 times. One of this is when they are at 9. For the rest 8 times, they will point together at times when minute m and hour h are related by the function,

m = h x (63/8)

ie., m = h x 7.875

So the times when the two hands of the clock will point in the same direction are,

1 hour and 1 x 7.875 min = 1 h: 7.88 min

2 hour and 2 x 7.875 min = 2 h: 15.75 min

3 hour and 3 x 7.875 min = 3 h: 23.63 min

4 hour and 4 x 7.875 min = 4 h: 31.50 min

5 hour and 5 x 7.875 min = 5 h: 39.38 min

6 hour and 6 x 7.875 min = 6 h: 47.25 min

7 hour and 7 x 7.875 min = 7 h: 55.13 min

8 hour and 8 x 7.875 min = 9 h: 00.00 min

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