Question

A traveller walking at 4 kilometres an hour can cover a distance in 2 hours 45 minutes on foot . By a cycle he covers it in only 40 minutes. Find his speed on the cycle?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

• Speed while walking = 4km/hr

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• Walked for 2hr 45 min

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• Time required to cover same distance while cycling is 40 minutes

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$\red{\underline \bold{To \: Find:}}$

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• Speed on cycle

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the speed on cycle be "x"

• Let the distance be "y"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\underline{\bold{\texttt {We know that :}}}$

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$\bf \dag \ \ Distance = Speed \times Time$

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Case I [ On foot ]

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• Speed = 4 km/hr

• Distance = y

• Time = 2hr 45 minutes

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$\sf \longmapsto y = 4 \times 2hr 45 minutes$

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$\sf \longmapsto y = 4 \times 2 \dfrac { 3 } { 4 }$

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$\sf \longmapsto y = 4 \times \dfrac { 11 } { 4 }$

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$\sf \dashrightarrow y = 11 km$

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• Hence distance will be 11 km

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Case II [ On cycle ]

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• Speed = x

• Distance = y

• Time = 40 minutes

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$\sf \longmapsto y = x \times 40 minutes$

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$\sf \longmapsto y = x \times \dfrac { 2 } { 3 }$

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$\sf \longmapsto 11 = x \times \dfrac { 2 } { 3 }$

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$\sf \longmapsto 33 = 2x$

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$\sf \longmapsto x = \dfrac { 33 } { 2 }$

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$\bf \dashrightarrow x = 16.5 km/hr$

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• Hence speed while cycling must be 16.5 km/hr to cover the same distance while walking.