Question

$\bigstar \: \boxed{Question} \: \bigstar$
Distance between Sanna's and Sneha's house is 9km. Sanna has to attend Sneha's birthday party at 7 o'clock. She started from her home at 6 o'clock on her bicycle and covered a distance of 6km in 40 mins. At the point she meet Micky and spoke to her for 5 mins and reached Sneha's birthday party at 7 o'clock. With what speed did she cover the second part of the journey ? Calculate his average speed for the entire journey.
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Answer 1

Given:

Distance between Sanna's and Sneha's house is 9km. Sanna has to attend Sneha's birthday party at 7 o'clock. She started from her home at 6 o'clock on her bicycle and covered a distance of 6km in 40 mins. At the point she meet Micky and spoke to her for 5 mins and reached Sneha's birthday party at 7 o'clock.

To find:

With what speed did she cover the second part of the journey? Calculate his average speed for the entire journey.

Concept:

If a person has a average speed along the course of the journey, its motion can be understood by calculating average speed. Average speed by the person can be calculated by using the following formula:

$\;\;\boxed{\:\textbf{\textsf{Average Speed = }} \dfrac{\textbf{\textsf{Total Distance}}}{\textbf{\textsf{Total Time\:}}}}$

This implies "Average speed is the ratio of total distance and total time taken to cover the distance."

Calculations:

Distance left to reach Sneha's house = 9km - 6km = 3km

And, Time left to reach Sneha's house = 16 min - (4 + 5) = 15 minutes

• Distance left = 3km

• Time left = 15 mins

The speed with which Sanna covered the second part of the journey:

$\rm{\implies\dfrac{Distance\;left\;to\;reach\;Sneha's\;house}{Time\;left\;to\;reach\;Sneha's\;house}}$

$\rm{\implies\dfrac{3}{15}}$

$\rm{\implies 0.2}$

Thus, the speed with which Sanna covered the second part of the journey is 0.2km/h.

We know that,

$\rm{\implies Average\;Speed=\dfrac{Total\; Distance}{Total\;Time}}$

• Total distance = 9km

• Total time = 1 hour

By substituting the given values in the formula, we get the following results:

$\rm{\implies Average\;Speed=\dfrac{9}{1}}$

$\rm{\implies \boxed{\textsf{\textbf{ Average Speed = 9 km/h }}}}$

Hence, the average speed of the entire journey is 9km/h.

$\rule{300}{2}$

Extra Information:

Average velocity is the displacement of an object over time. It is calculated by using the following formula:

$\;\;\boxed{\:\textbf{\textsf{Average Velocity = }} \dfrac{\textbf{\textsf{Total Displacement}}}{\textbf{\textsf{Total Time\:}}}}$

This implies "Average velocity the change in position or displacement (Δx) divided by the change in time or time intervals (Δt)."

Answer 2

$\star \; {\underline{\boxed{\purple{\pmb{\frak{ \; Given \; :- }}}}}}$

• Distance = 9 km
• Started her Journey = 6 O'clock
• Has to Reach = 7 O'clock
• Distance Covered by Cycle = 6 km
• Time Taken by Cycle = 40 mins
• Talked to Micky = 5 mins

$\star \; {\underline{\boxed{\orange{\pmb{\frak{ \; To \; Find \; :- }}}}}}$

• Speed of Second Part
• Average Speed

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\green{\pmb{\frak{ \; SolutioN \; :- }}}}}}$

☆ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Speed = \dfrac{ Distance }{ Time } }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Average \; Speed = \dfrac{ Total \; Distance }{ Total \; Time } }}}}}$

☆ Examining the Second Part :

• Distance Left = 9 km - 6 km = 3 km
• Time Left = 60 min - (40 + 5) min = 15 min

☆ Calculating the Speed :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Speed = \dfrac{ Distance }{ Time } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Speed = \dfrac{ 3 }{ 15 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Speed = \cancel\dfrac{ 3 }{ 15 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf { Speed = 0.2 \; km/h }}}}} \; {\green{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

☆ Calculating the Average Speed :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Average \; Speed = \dfrac{ Total \; Distance }{ Total \; Time } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Average \; Speed = \dfrac{ 9 }{ 1 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Average \; Speed = \cancel\dfrac{ 9 }{ 1 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf { Average \; Speed = 9 \; km/h }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Sanna travelled the 2nd Part with the Speed of 0.2 km/h and the Average Speed of her Journey is 9 km/h .

$\\ \qquad{\rule{200pt}{2pt}}$