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| 1 | +convert_prompt_example = ( # noqa: E501 |
| 2 | + "<|begin_of_thought|>\n\n" |
| 3 | + "Okay, so I've got this problem here. Mr. Wang leaves home at 6 AM, riding his bike at 12 km/h, " |
| 4 | + "and he stops to rest for 6 minutes after every 30 minutes of riding. Then, when he arrives at a park " |
| 5 | + "that's 16.8 km away, I need to find out the angle between the hour and minute hands on his watch.\n\n" |
| 6 | + "Alright, first things first, I need to figure out how long it takes Mr. Wang to ride 16.8 km, including " |
| 7 | + "his rest periods.\n\n" |
| 8 | + "So, his speed is 12 km/h. To find out how long it takes to go 16.8 km without any stops, I can use the formula " |
| 9 | + "time = distance/speed. That would be 16.8 divided by 12, which is 1.4 hours. To make it easier, that's 1 hour and 24 minutes.\n\n" |
| 10 | + "But wait, he doesn't ride straight through. He stops for 6 minutes after every 30 minutes of riding. So, I need to see how many " |
| 11 | + "of those 30-minute riding periods are there in his total riding time.\n\n" |
| 12 | + "In 1 hour and 24 minutes of riding, how many 30-minute segments are there? Well, 1 hour is 60 minutes, plus 24 minutes makes 84 minutes " |
| 13 | + "total riding time. So, 84 divided by 30 is 2.8. That means he has two full 30-minute riding periods and a partial one.\n\n" |
| 14 | + "After each full 30-minute riding period, he rests for 6 minutes. So, for two full periods, he rests twice, which is 12 minutes of rest.\n\n" |
| 15 | + "Now, for the partial riding period. Since 2 times 30 minutes is 60 minutes, and he has 84 minutes of riding, the remaining riding time is 84 minus 60, " |
| 16 | + "which is 24 minutes. So, he rides for 24 minutes without another rest because he doesn't complete another 30-minute segment.\n\n" |
| 17 | + "So, total time taken is riding time plus rest time. That's 84 minutes riding plus 12 minutes resting, totaling 96 minutes.\n\n" |
| 18 | + "Wait a minute, but he stops after every 30 minutes of riding, but in the last partial period of 24 minutes, does he rest again? I think he only rests after " # noqa: E501 |
| 19 | + "completing 30 minutes of riding, so in this case, since the last riding period is only 24 minutes, he doesn't take an additional rest after that.\n\n" |
| 20 | + "So, total time should be 84 minutes riding plus 12 minutes resting, which is indeed 96 minutes, or 1 hour and 36 minutes.\n\n" |
| 21 | + "So, he leaves at 6 AM and takes 1 hour and 36 minutes to reach the park, arriving at 7:36 AM.\n\n" |
| 22 | + "Now, I need to find the angle between the hour and minute hands at 7:36.\n\n" |
| 23 | + "To find the angle between the hour and minute hands, I can use the formula:\n\n" |
| 24 | + "|30H - 5.5M|\n\n" |
| 25 | + "where H is the hour and M is the minutes.\n\n" |
| 26 | + "At 7:36, H is 7 and M is 36.\n\n" |
| 27 | + "So, plugging in:\n\n" |
| 28 | + "30*7 = 210\n\n" |
| 29 | + "5.5*36 = 198\n\n" |
| 30 | + "210 - 198 = 12\n\n" |
| 31 | + "So, the angle is 12 degrees.\n\n" |
| 32 | + "Wait, but I should make sure that's the smaller angle. Sometimes, the larger angle is considered, but usually, the smaller one is what is asked for.\n\n" |
| 33 | + "So, the angle between the hour and minute hands at 7:36 AM is 12 degrees.\n\n" |
| 34 | + "I think that's the answer.<|end_of_thought|>\n\n" |
| 35 | + "<|begin_of_solution|>\n\n" |
| 36 | + "Mr. Wang leaves home at 6 AM and rides at a speed of 12 km/h, stopping to rest for 6 minutes after every 30 minutes of riding. " |
| 37 | + "He arrives at a park 16.8 km away. To determine the angle between the hour and minute hands on his watch when he arrives, we first calculate the total time taken.\n\n" # noqa: E501 |
| 38 | + "1. **Riding time without stops**:\n\n" |
| 39 | + "$$\\text{Time} = \\frac{\\text{Distance}}{\\text{Speed}} = \\frac{16.8 \\text{ km}}{12 \\text{ km/h}} = 1.4 \\text{ hours} = 84 \\text{ minutes}$$\n\n" |
| 40 | + "2. **Rest periods**:\n\n" |
| 41 | + " - He rests for 6 minutes after every 30 minutes of riding.\n\n" |
| 42 | + " - In 84 minutes of riding, he completes 2 full 30-minute segments and a partial 24-minute segment.\n\n" |
| 43 | + " - He rests twice, totaling 12 minutes of rest.\n\n" |
| 44 | + "3. **Total time**:\n\n" |
| 45 | + "$$\\text{Total time} = 84 \\text{ minutes (riding)} + 12 \\text{ minutes (rest)} = 96 \\text{ minutes} = 1 \\text{ hour and } 36 \\text{ minutes}$$\n\n" |
| 46 | + " - He arrives at 7:36 AM.\n\n" |
| 47 | + "4. **Angle between hour and minute hands at 7:36**:\n\n" |
| 48 | + " - Use the formula:\n\n" |
| 49 | + "$$\\text{Angle} = |30H - 5.5M|$$\n\n" |
| 50 | + " - At 7:36, $H = 7$ and $M = 36$:\n\n" |
| 51 | + "$$\\text{Angle} = |30 \\times 7 - 5.5 \\times 36| = |210 - 198| = 12 \\text{ degrees}$$\n\n" |
| 52 | + "Thus, the angle between the hour and minute hands on his watch is $\\boxed{12}$.<|end_of_solution|>\n" # noqa: E501 |
| 53 | +) |
| 54 | + |
| 55 | +# From https://arxiv.org/pdf/2412.09413 |
| 56 | +CONVERT_PROMPT = ( |
| 57 | + "Another solution is written in an unstructured way. Your job is to convert them into two sections:" |
| 58 | + "<|begin_of_thought|>" |
| 59 | + "(Thought process, you should copy exactly the thinking process of the original solution.)" |
| 60 | + "<|end_of_thought|>" |
| 61 | + "<|begin_of_solution|>" |
| 62 | + "(Final formatted, precise, and clear solution; make sure there is only one solution in this section; If it is a coding problem, make sure there is only one code block)" # noqa: E501 |
| 63 | + "<|end_of_solution|>" |
| 64 | + "Here is an example demonstration of a different question, you can refer to its format: " |
| 65 | + "{example}\n" |
| 66 | + "Important: You should almost copy all the contents word-by-word of the original solution. Just convert them into two sections. " |
| 67 | + "Make sure you include: <|begin_of_slow_thought|>, <|end_of_slow_thought|>, <|begin_of_solution|>,<|end_of_solution|> These four headers explicitly. " |
| 68 | + "Content to be converted: {{content}}".format(example=convert_prompt_example) |
| 69 | +) |
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