# Clock Problem

Clock-related Problems in Algebra

## Time After 7:00 O'clock When The Minute & Hour Hands Of The Clock Are Together

**Problem**

What time after 7:00 o’clock will the hands of a continuously driven clock are together?

## 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?

**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.

Key equations:

$\dfrac{x}{12}$ = 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.