Question

On a 120 km track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel the next 90 km so as to average 60 km/h for the entire trip?
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Answer with explanation !!~​

Answer 1

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

• Total Distance = 120 km
• Initial Distance = 30 km
• Speed = 30 km/h
• Distance Left = 90 km
• Average Speed = 60 km/h

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

• Speed of Rest Distance = ?

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

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

$\dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Time \; for \; A_{ve} \; Distance \; :- }}}}$

$\begin{gathered} \; \; \color{darkblue}\dashrightarrow \; \; {\red{\sf{ Time = \dfrac{Distance}{Speed} }}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ Time = \dfrac{30}{30} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ Time = \cancel\dfrac{30}{30} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak{ Time = 1 \; hr }}}}} \; \green\bigstar \\ \\ \\ \end{gathered}$

$\dag \; {\underline{\underline{\sf{ \; Now \; we \; Have \; :- }}}}$

• Total Distance = 120 km
• Average Speed = 60 km/h

$\dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Time \; :- }}}}$

$\begin{gathered} \; \; \color{darkblue}\longrightarrow \; \; {\red{\sf{ Total \; Time = \dfrac{Total \; Distance}{A_{ve} \; Speed} }}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf{ Total \; Time = \dfrac{120}{60} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf{ Total \; Time = \cancel\dfrac{120}{60} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; {\underline{\boxed{\pmb{\frak{ Time = 2 \; hrs }}}}} \; \pink\bigstar \\ \\ \\ \end{gathered}$

$\dag \; {\underline{\underline{\sf{ \; Now \; we \; Have \; :- }}}}$

• Remaining Distance = 90 km
• Time Left = 2 - 1 = 1 hr

$\dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Speed \; Required \; :- }}}}$

$\begin{gathered} \; \; \color{darkblue}\implies \; \; {\red{\sf{ Speed = \dfrac{Distance}{Time} }}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; \sf{ Speed = \dfrac{90}{1} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; \sf{ Speed = \cancel\dfrac{90}{1} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; {\underline{\boxed{\pmb{\frak{ Speed \; Required = 90 \; km/h }}}}} \; \purple\bigstar \\ \\ \\ \end{gathered}$

$\therefore \;$ Speed Required for the Rest of thr trip is 90 km/h .

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

Answer 2

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

• Distance : 120 km

• 1 St hour = uniform speed of 30km/hr

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

• Speed of train for next 90Km/h

$\star\;{\underline{\boxed{\pmb{\blue{\frak{\; Solution\; :-}}}}}}$

$\sf\huge\star$ Concept

$\rightarrow$In this numerical we have given Total distance travelled by a train that is 120 km and the average speed of the train for the whole journey i.e 60 km /h .From this we can find the total time taken by the train to complete whole journey.

This can be done as follows :

Average speed = $\dfrac{Total \: Distance\: travelled}{Total\:Time\:taken}$

So ,

$\Huge\sf\implies$ 60 = $\dfrac{120}{Total\:time\:taken}$

$\huge\sf\rightarrow$ Time taken

$\dfrac{120}{60}$

$\Huge\sf\implies$ $\star\;{\underline{\boxed{\pmb{\pink{\frak{\;2 hours\; :-}}}}}}$

In first hour it travelled 30km as it speed was 30 km /hr

So the time taken by it to travel 90 km was

$\huge\rightarrow$ 2 hr - 1 hr = 1 hr

So , it's speed in 2nd case was

$\Huge\sf\implies$ $\bold\color{orange}{Distance\:÷\:Time\:taken}$

$\Huge\sf\implies$ 90 ÷ 1

$\Huge\sf\implies$$\star\;{\underline{\boxed{\pmb{\green{\frak{\;90km/hr\; :-}}}}}}$

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