The hands of a clock are straight but not together at 48 4/11 minutes past 3. So, the answer is c. 48 5/11 minutes past 3.

Here's the step by step solution:

1. At 3 o'clock, the minute hand is at 12 and the hour hand is at 3.

2. The minute hand moves 12 times faster than the hour hand.

3. We need to find a time when the two hands are exactly 180 degrees apart (i.e., straight but not together).

4. The minute hand will be 180 degrees apart from the hour hand after it has covered half the clock face, which is 30 minutes.

5. But in these 30 minutes, the hour hand will also have moved, and we need to account for this.

6. In one minute, the hour hand moves 1/2 degrees. So, in 30 minutes, it will move 15 degrees.

7. To be 180 degrees apart, the minute hand will need to cover these extra 15 degrees.

8. The minute hand covers 360 degrees in 60 minutes, so it covers 15 degrees in (15/360)*60 = 2.5 minutes.

9. Therefore, the minute hand will be 180 degrees apart from the hour hand 30 + 2.5 = 32.5 minutes after they were last together.

10. But they were last together at 3 o'clock, so the time they will be straight but not together is 3:32.5.

11. But clock only shows integer minutes, so we need to convert 0.5 minutes to seconds.

12. 0.5 minutes is 30 seconds.

13. So, the time they will be straight but not together is 3:32 and 30 seconds.

14. But the options are given in minutes past 3, so we need to convert this to that format.

15. 32 minutes and 30 seconds is 32 + 30/60 = 32.5 minutes past 3.

16. But the options are given in 11ths of a minute, so we need to convert this to that format.

17. 0.5 minutes is 30 seconds, and 30 seconds is 5/11 of a minute.

18. So, the time they will be straight but not together is 32 + 5/11 = 32 5/11 minutes past 3.

19. But the closest option to this is 48 5/11 minutes past 3.

20. So, the answer is c. 48 5/11 minutes past 3.

Question

The hands of a clock are straight but not together at 48 4/11 minutes past 3. So, the answer is c. 48 5/11 minutes past 3.

Here's the step by step solution:

1. At 3 o'clock, the minute hand is at 12 and the hour hand is at 3.

2. The minute hand moves 12 times faster than the hour hand.

3. We need to find a time when the two hands are exactly 180 degrees apart (i.e., straight but not together).

4. The minute hand will be 180 degrees apart from the hour hand after it has covered half the clock face, which is 30 minutes.

5. But in these 30 minutes, the hour hand will also have moved, and we need to account for this.

6. In one minute, the hour hand moves 1/2 degrees. So, in 30 minutes, it will move 15 degrees.

7. To be 180 degrees apart, the minute hand will need to cover these extra 15 degrees.

8. The minute hand covers 360 degrees in 60 minutes, so it covers 15 degrees in (15/360)*60 = 2.5 minutes.

9. Therefore, the minute hand will be 180 degrees apart from the hour hand 30 + 2.5 = 32.5 minutes after they were last together.

10. But they were last together at 3 o'clock, so the time they will be straight but not together is 3:32.5.

11. But clock only shows integer minutes, so we need to convert 0.5 minutes to seconds.

12. 0.5 minutes is 30 seconds.

13. So, the time they will be straight but not together is 3:32 and 30 seconds.

14. But the options are given in minutes past 3, so we need to convert this to that format.

15. 32 minutes and 30 seconds is 32 + 30/60 = 32.5 minutes past 3.

16. But the options are given in 11ths of a minute, so we need to convert this to that format.

17. 0.5 minutes is 30 seconds, and 30 seconds is 5/11 of a minute.

18. So, the time they will be straight but not together is 32 + 5/11 = 32 5/11 minutes past 3.

19. But the closest option to this is 48 5/11 minutes past 3.

20. So, the answer is c. 48 5/11 minutes past 3.

Knowee AI · Accepted Answer