Clock Problem

Clock-related Problems in Algebra

The Hour Hand And Minute Hand Of The Clock Exchanged Places

Problem
Between 3:00 and 4:00, Kathryn looked at her watch and noticed that the minute hand was between 5 and 6. Later, Kathryn looked again and noticed that the hour hand and the minute hand had exchanged places. What time was it in the second case?
 

Time After 3:00 O'clock When The Hands Of The Clock Are Perpendicular

Problem
How many minutes after 3:00 o’clock will the hands of the clock be perpendicular to each other for the 1st time?

A.   35 C.   32.73
B.   33.15 D.   34.12

 

Time When The Angle Between The Hands Of The Clock Were Bisected By The 3 O'clock Mark

Problem
What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?

A. 2:18:27.6
B. 2:16:00.0
C. 2:17:56.3
D. 2:19:03.1
 

Clock-related Problems

There are 12 dial units in the clock. Every time the minute hand completes 12 dials, the hour hand moves 1 dial. Thus, if the minute hand moves by x the hour hand moves by x/12.
 

000-clock-problem-illustration.gif

 

Key equations:

$x$ = distance traveled by the minute hand (in minutes)

$\dfrac{x}{12}$ = distance traveled by the hour hand (in minutes)

 

Verbal Problems in Algebra

The following is an attempt to classify the verbal problems.
 

Number-related problems
Number-related problems are considered as the most basic type of verbal problems. It is taken as the base point of analysis for more complex type of problems.
 

Digit-related problems

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