Question 7
Alice enters the world through the looking glass. This time, she has turned back time to save the Mad Hatter. The White Queen warns her: “If you do not put the metal sphere back into the machine before the minute and hour hands coincide, everything will be destroyed.” The clock now shows exactly 5 o’clock. How much time does Alice have to save the Mad Hatter before everything is destroyed? Let us answer the following questions to find the solution!
1. In one hour, how many complete turns does the minute hand make, and how many does the hour hand make? How many more turns does the minute hand make than the hour hand in each hour?
2. At 5 o’clock, which numbers do the hour and minute hands point to, respectively? At 5 o’clock, how many turns ahead of the minute hand is the hour hand?
3. From 5 o’clock until the hands first coincide, how many more turns does the minute hand make than the hour hand?
4. Using your answers above, calculate the shortest time after 5 o’clock until the minute and hour hands coincide. Thus, how much time does Alice have to save the Mad Hatter?
1. In one hour, how many complete turns does the minute hand make, and how many does the hour hand make? How many more turns does the minute hand make than the hour hand in each hour?
2. At 5 o’clock, which numbers do the hour and minute hands point to, respectively? At 5 o’clock, how many turns ahead of the minute hand is the hour hand?
3. From 5 o’clock until the hands first coincide, how many more turns does the minute hand make than the hour hand?
4. Using your answers above, calculate the shortest time after 5 o’clock until the minute and hour hands coincide. Thus, how much time does Alice have to save the Mad Hatter?