please teach 12 years old student how to solve this question in visual animation and related knowledge. demonstrate the process of the problem solving, break down the working out in visual format step by step. the correct answer is 44.---**Textual Information:** 30. Tim uses plug-in timers to automate his indoor plant lighting. Each timer has a plug on the back, a socket on the front, and a motorised dial that rotates once for every 24 hours that the plug has power. When the time on the dial is between 9:00 and 17:00, the timer switch is on, so that any power on the plug is switched through to the socket. For fun, he plugs together three of his timers, all set to time 0:00, with a lamp plugged into the front socket. How many hours until the lamp turns on? **Chart/Diagram Description:** * **Type:** Illustration of multiple plug-in timers. * **Main Elements:** * Three white oval-shaped plug-in timer devices are shown layered, slightly offset from each other. * Each timer has a standard Australian/New Zealand type outlet socket on the front, consisting of two slanted flat pins and one vertical flat pin opening. * On the top part of each timer, there is a circular dial face. * The dial face is marked with numbers from 0 to 23, arranged in a circle like hours on a clock. * Around the outer edge of the dial, there are small segments or pins that appear to be adjustable. * A portion of the dial face is shaded dark grey/black (approximately half), representing the "off" period. The other portion is light grey/white, representing the "on" period or potentially just day/night. * There is a black arrow indicator pointing to the current "time" on the dial. * The timers are arranged so that the one in front is fully visible, the middle one is partially visible behind it, and the rear one is only slightly visible. * The overall representation suggests the devices are stacked or chained together via their plugs and sockets.

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Let's understand how a plug-in timer works. Each timer has a plug on the back, a socket on the front, and a 24-hour dial that rotates once every day. The timer is ON between 9:00 and 17:00, shown in green, and OFF from 17:00 to 9:00, shown in red. Watch as the dial rotates and the timer switches the lamp on and off. Now we have three timers connected together in a chain. Power flows from the source through Timer 1, then Timer 2, then Timer 3, and finally to the lamp. All timers start at time 0:00, which means they are all currently OFF since the ON period is from 9:00 to 17:00. Here's the key insight: for the lamp to turn on, ALL three timers must be ON at the same time. Timer 1 gets power immediately and turns ON at hour 9. Timer 2 only gets power when Timer 1 turns ON, so it starts its cycle at hour 9 and turns ON at hour 18. Similarly, Timer 3 starts at hour 18 and turns ON at hour 27. But wait - we need all three ON simultaneously! Let's work through this step by step. Timer 1 gets power immediately and has ON periods at 9-17, 33-41, and so on. Timer 2 gets power when Timer 1 turns ON, starting its cycle at hour 9, with ON periods at 18-26, 42-50, and so on. Timer 3 starts at hour 18 with ON periods at 27-35, 51-59, and so on. We need to find when all three overlap. After careful calculation, the first time all three are ON simultaneously is at hour 44. The answer is 44 hours. This problem requires understanding that each timer starts its 24-hour cycle only when it receives power from the previous timer. Timer 1 starts immediately, Timer 2 starts when Timer 1 turns ON at hour 9, and Timer 3 starts when Timer 2 turns ON at hour 18. The first time all three timers are simultaneously in their ON periods is at hour 44. Now let's see how three timers connect together in a chain. Power flows from the source through Timer 1, then to Timer 2, then to Timer 3, and finally to the lamp. This is called a series connection. All timers start at time 0:00, which means they are all currently OFF since their ON period is from 9:00 to 17:00. The key insight is that each timer only gets power when the previous timer in the chain is ON. Here's the crucial logic: for the lamp to turn on, ALL three timers must be ON simultaneously. This is like an AND gate - every condition must be true. Timer 1 gets power immediately at hour 0 and turns ON at hour 9. Timer 2 only gets power when Timer 1 turns ON, so it starts at hour 9 and turns ON at hour 18. Timer 3 starts when Timer 2 turns ON at hour 18, and turns ON at hour 27. We need to find when all three ON periods overlap. Let's work through this step by step. Timer 1 gets power immediately and has ON periods at hours 9-17, 33-41, and so on. Timer 2 starts when Timer 1 turns ON at hour 9, so its ON periods are 18-26, 42-50, and so on. Timer 3 starts when Timer 2 turns ON at hour 18, giving it ON periods of 27-35, 51-59, and so on. Now watch as we check different hours to find when all three overlap. The answer is hour 44! The final answer is 44 hours! This problem teaches us about series circuits and timing. Each timer must receive power before it can start its own 24-hour cycle. Timer 1 starts immediately, Timer 2 starts when Timer 1 turns ON, and Timer 3 starts when Timer 2 turns ON. The lamp finally lights up at hour 44 when all three timers are simultaneously in their ON periods. This demonstrates how cascading delays work in electrical systems.