[Math] Minute Hand will be as much ahead of the hour Hand as it is Behind it

algebra-precalculus

The time is past 2 o'clock in 10 minutes. The minute hand will be as much as ahead of the hour hand as it is behind it. What time is it?

The Answer is 2:05.91

I am having trouble interpreting " Minute Hand will be as much ahead of the hour Hand as it is Behind it ". Does it mean the hour hand somehow bisects the two times of the minute hand? I am more of a visual learner… but i dont know why clock problems for me are so hard to visualize. maybe there is an easier way?

Best Answer

Here is how I would interpret the question: "The time is past 2 o'clock. In 10 minutes, the minute hand will be as much ahead of the hour hand as it is behind it [right now]." It's not quite right to say that the hour hand bisects the two positions of the minute hand, since the hour hand is also moving, but you're on the right track. Here is what we can infer:

  • Right now the minute hand is behind the hour hand (in particular, it is probably between 2:00 and 2:10).
  • In ten minutes the minute hand will be in front of the hour hand.
  • The distance right now between the minute hand and the hour hand is the same as the distance between them will be in ten minutes.

These points make 2:05.91 seem like a reasonable answer, although I'll admit that I'm getting a slightly different answer when I work the problem myself.

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