Question

A man travels 14 hours and 40 minutes. Half of the journey is in train at a speed of 60 km/hr and remaining half is in road at a speed of 50 km/hr. Distance travelled is...? ​

Answer 1

Given: Total time taken by man to cover total distance is 14 hours 40 minutes.

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☯ Let Total distance travelled by Man be x km.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Speed = \dfrac{Distance}{Time}}}}}\\ \\ \\ :\implies\sf Time = \dfrac{Distance}{Speed}$

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies\sf 14 \dfrac{40}{60} = \dfrac{ \frac{x}{2}}{60} + \dfrac{ \frac{x}{2}}{50}$

$:\implies\sf 14 \dfrac{2}{3} = \dfrac{x}{120} + \dfrac{x}{100}$

$:\implies\sf \dfrac{44}{3} = \dfrac{100x + 120x}{12000}$

$:\implies\sf \dfrac{44}{3} = \dfrac{220x}{12000}$

$:\implies\sf \dfrac{44}{ \cancel{3}} \times \cancel{12000} = 220x$

$:\implies\sf 44 \times 4000 = 220x$

$:\implies\sf 176000 = 220x$

$:\implies\sf x = \cancel{ \dfrac{176000}{220}}$

$:\implies{\underline{\boxed{\frak{\purple{x = 800}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:Total\:distance\:travelled\:by\:man\:is\: {\textsf{\textbf{800\:km}}}.}}}$

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: More\: to \: know :}}}}}\mid}$

• Distance: The complete length of the path between any two points is called distance.

• Distance is denoted by "d".

• Distance is a scalar quantity as it only depends upon the magnitude and not the direction.

• The distance can only have positive values.

Answer 2

$\underline{\underline{\sf{\ddag\qquad Required \: AnsWer :\qquad \ddag}}}$

Let the total distance travelled be 2x km.

$\spadesuit\:\underline{\frak{Convert \: the \: time \: total \: taken \: in \: Fraction: }}$

$:\implies \sf Total \: time = 14 \: hours \: and \: 40 \: minutes$

$:\implies \sf Total \: time =14 \dfrac{40}{60} \: hours$

$:\implies \sf Total \: time =14 \dfrac{4}{6} \: hours$

$:\implies \sf Total \: time =14 \dfrac{2}{3} \: hours$

$:\implies\underline{\boxed{ \sf Total \: time = \dfrac{44}{3} \: hours }}$

$\therefore\:\underline{\textsf{The total time taken by the man is \textbf{ \dfrac{\text {44}}{\text 3} hours}}}.$

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☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\dashrightarrow\:\:\sf Time = \dfrac{Distance}{Speed}$

$\dashrightarrow\:\:\sf \dfrac{44}{3} = \dfrac{x}{60} + \dfrac{x}{50}$

$\dashrightarrow\:\:\sf \dfrac{44}{3} = \dfrac{50x + 60x}{3000}$

$\dashrightarrow\:\:\sf \dfrac{44}{3} = \dfrac{5x + 6x}{300}$

$\dashrightarrow\:\:\sf \dfrac{44}{3} = \dfrac{11x}{300}$

$\dashrightarrow\:\:\sf \dfrac{44 \times 300}{3} = 11x$

$\dashrightarrow\:\:\sf \dfrac{13200}{3} = 11x$

$\dashrightarrow\:\:\sf 4400 = 11x$

$\dashrightarrow\:\:\sf x = \dfrac{4400}{11}$

$\dashrightarrow\:\: \underline{ \boxed{\sf x = 400}}$

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$\longrightarrow\:\:\sf Total \: distance = 2x$

$\longrightarrow\:\:\sf Total \: distance = 2 \times 400$

$\longrightarrow\:\: \underline{ \boxed{\sf Total \: distance = 800 \: km}}$

$\therefore\:\underline{\textsf{The total distance travelled by the man is \textbf{800 km}}}.$