Clock word problem.

4. On planet X, their clocks have only 9 hours, and each hour contains 63

minutes. Determine all the times (up to two decimal places) when the hands

of a clock on planet X have both hands pointing in exactly the same direction.

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In a clock having 9 hours, having 63 minutes each, will have 9-1=8 positions when both the hands point exactly in the same direction.

Time interval between such positions = 9/8 = 1.125hour

=> =1 hour 0.125*63min = 1hr 7.875min

So the first time = 1 hour 7.88 minutes = 1:07.88

Second = 2*(1hr 7.875mim) = 2Hours 15.75 minutes = 2:15.75

Third = 3*(1hr 7.875mim) = 3Hours 23.63 minutes = 3:23.63

Forth = 4*(1hr 7.875mim) = 4Hours 31.50 minutes = 4:31.50

Fifth = 5*(1hr 7.875mim) = 5Hours 39.38 minutes = 5:39.38

Sixth = 6*(1hr 7.875mim) = 6Hours 47.25 minutes = 6:47.25

Seventh = 7*(1hr 7.875mim) = 7Hours 55.13 minutes = 7:55.13

Eighth = 8*(1hr 7.875mim) = 8Hours 63 minutes = 9:00.00

**Timing when both arms of clock point in the same direction are**

**1:07.88, 2:15.75, 3:23.63, 4:31.50, 5:39.38, 6:47.25, 7:55.13 and 9:00.00**

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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