Expert: Paul Klarreich - 9/25/2007

Question
QUESTION: What is the ratio between the hour hand and the minute hand of a clock at 2:15?

ANSWER: Questioner:   Lee Ann
Category:  Advanced Math
Private:  No
 
Subject:  ratios
Question:  What is the ratio between the hour hand and the minute hand of a clock at 2:15?
....................................
Hi, Lee Ann,

Are you sure you mean the 'ratio'?  I know the minute hand is longer, but exactly how much longer???

I think, instead, you mean the ANGLE between the hands.  For this, you just determine the rotation of each hand:

The hour hand rotates 360 degrees in 12 hours, or 30 degrees each hour, starting at the 12:00 position, due North.  

In 2 and 1/4 hours (that's 2:15) it has rotated 67.5 degrees.

The minute hand rotates 360 degrees in ONE hour, or 6 degrees per minute, starting at due North.  In 15 minutes it has rotated 90 degrees.

The angle between them is  90 - 67.5 = 22.5 degrees.


---------- FOLLOW-UP ----------

QUESTION: Hi, thanks for the info but I do mean ratio.  This was an interview question at a broker firm.  2/3 is my guess but I'm not even sure what they are asking.

Answer
Questioner:   Lee Ann
Category:  Advanced Math
Private:  No
 
Subject:  Angles
Question:  QUESTION: What is the ratio between the hour hand and the minute hand of a clock at 2:15?

ANSWER: Questioner:   Lee Ann
Category:  Advanced Math
Private:  No

Subject:  ratios
Question:  What is the ratio between the hour hand and the minute hand of a clock at 2:15?
....................................
Hi, Lee Ann,

Are you sure you mean the 'ratio'?  I know the minute hand is longer, but exactly how much longer???

I think, instead, you mean the ANGLE between the hands.  For this, you just determine the rotation of each hand:

The hour hand rotates 360 degrees in 12 hours, or 30 degrees each hour, starting at the 12:00 position, due North.  

In 2 and 1/4 hours (that's 2:15) it has rotated 67.5 degrees.

The minute hand rotates 360 degrees in ONE hour, or 6 degrees per minute, starting at due North.  In 15 minutes it has rotated 90 degrees.

The angle between them is  90 - 67.5 = 22.5 degrees.


---------- FOLLOW-UP ----------

QUESTION: Hi, thanks for the info but I do mean ratio.  This was an interview question at a broker firm.  2/3 is my guess but I'm not even sure what they are asking.
======================================================

Hi, Lee Ann,

Neither am I.  If this is how the firm thinks, could you please give me their name?  Then I can look up their recommendations and be sure to do the opposite.