List of high-quality authors
It's so hard!Stumped a big piece!Grade 6 Questions: Hour and Minute Hands Chasing Problems!
As shown in Figure 1,
It's 6 o'clock sharp, and between 6 and 7 o'clock, when will the minute hand be exactly perpendicular to the hour hand?
The difficulty of this question is:How to express the actual problem in mathematical language, that is, transform it into a more understandable mathematical problem?
Essentially, it's a chase problem!
For example, this can be translated into the following equivalent math problem
Two snails A and B chase each other along the 60cm long runway in a loop, A and B are 30cm apart, A is in front and B is behind, A crawls 1 12cm per minute, B crawls 1cm per minute, and asks when A and B are 15cm apart within 1 hour.
Obviously, question 2 is equivalent to question 1, but question 2 is simpler, more intuitive, and easier to understand than question 1!
Resolution of Question 2:
B crawls 11 12 cm more per minute than A.
The first time is 15 cm apart, A is still in front of B and B is still behind, at this time B crawls 15 cm more than A, so the time required is 15 (11 12) = 16 and 4 11 minutes.
The second time is 15 cm apart, B overtakes A, and B crawls 45 cm more than A, so the time required is 45 (11 12) = 49 and 1 11 minutes.
Friends have good ideas or methods, welcome to leave a message to share!