# Math mini-contest problem for Day 8 on D.Buzz 😎

in D.Buzz3 months ago

Math problem for Day 8 😎

Holovision waits until 11:00 P.M. in his local time to answer Math problems. When he looked at the clock just after 10:00 P.M., he noticed its hour and minute hands pointing in opposite directions. How many exact minutes does he still need to wait?

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Sorry I forgot about yesterday's quiz.

Today my guess is 38.18 minutes.

Given a clock: Degree = 30*hour -11/2 minute
180=300-11/2m
m = 240/11 = 21.82 so the time is 21.82 seconds after 10:00.

I meant 21.82 minutes after 10:00.

Thus the the 38.18 I got is 60 - 21.82.

40 mins

Time is 10:20... 60-20=40 mins

# 38 2/11 minutes or 38.18 minutes 🎯

Either the fractional or decimal answer shall be considered as correct answer.

## Explanation

Context: The original problem is under clock problems in algebra. The problem specifically asks how many exact minutes must pass so that the minute and hour hands between 10:00 and 11:00 becomes exactly 11:00 (hour and minute hands are together). It does not matter if the time is A.M. or P.M.

Solution: An easy approach here is to first get the exact time between 10:00 and 11:00 where the minute and hour hands are in opposite directions (180° away from each other in either direction). At 10:00, the minute hand of the clock is 60° ahead of the hour hand. For the minute hand to be exactly 180° ahead of the hour hand, it must travel 120° or 20 minutes farther from the hour hand. (20 minutes) / (11/12) = 21 9/11 minutes or 21.82 minutes from 10:00. Therefore, the clock needs exactly 38 2/11 minutes or 38.18 minutes for its hands to represent 11:00.

For beginners: The 11/12 fraction represents the fact that whenever the minute hand moves 12 ticks [minutes], it gets only 11 ticks away from the hour hand. 1 tick = 1 minute = 5°

## Winner: @jfang003 🏅

1 HIVE has been sent to @jfang003's Hive account. 💰