It is spring, and there 12 hours of daylight. A caterpillar climbs a vertical wall at a speed of 1 foot per hour during the day, and then sleeps for the 12 hours of darkness, during which it slides downward at 1/2 foot per hour. The wall is 48 feet high. How long will it take the caterpillar to reach the top of the wall?

小提示：If the caterpillar reaches the top of the wall and naps, it will not slide down at all.

请用英语作答！尽可能用英语，如果实在表达不清楚，你可以在英文回答的同时辅以少量中文解释
答其然也要答其所以然！请一定把你的思维过程写出来喔~~

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