Chapter 1, Problem 30RP

To determine

To Find: Number of degrees covered by hour hand in $40$ minutes

Answer to Problem 30RP

Number of degrees covered by hour hand in $40$ minutes = $20°$

Explanation of Solution

Given information:In the figure K’s watch is given which shows time as $3:35$ and if K will reach by $4:15$ it means she will take $40$ minutes to reach home.

Calculation: As per the question K’s watch is given which shows time as $3:35$ and if K will reach by $4:15$ it means she will take $40$ minutes to reach home.

We know that a clock represents a complete circle having $360$ degrees. It is divided into $12$ equal parts i.e. each part is $\frac{360°}{12}=\text{ 30}°$

Further to this the hour hand covers just one part out of $12$ parts in one hour .This means it covers $30°$ in $60$ minutes i.e. $\frac{30°}{60}\text{ = }{\left(\frac{1}{2}\right)}^{°}$ per minute.

Thus, the number of degrees covered by hour hand in $1$ minute = $\frac{1}{2}$ degree

The number of degrees covered b hour hand in $40$ minutes = $\text{= }{\left(\frac{1}{2}\right)}^{°}\times \text{ 40 = 20}°$

Conclusion:

So, hour hand will travel $20°$ before K reach home.