Question

14. A boy covers a distance of 20 km in 2 hours, partly on foot at the rate of 5 km/hour and partly on bicycle at the rate of 10 km/hour. Find thedistance covered on foot.​

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Given- }}$

• Total distance covered = 20 km

• Total time taken = 2 hours

• Speed while covered the distance by foot = 5 km/ hour

• Speed while covered the distance by bicycle = 10 km per hour

$\large\underline{\sf{To\:Find - }}$

• The distance covered by foot.

$\large\underline{\sf{Solution-}}$

Let the distance covered by foot be 'x' km.

Total distance to be covered = 20 km

So,

Distance covered by bicycle = (20 - x) km

Case :- 1

We have

• Distance covered by foot = x km

• Speed during this = 5 km per hour

We know,

$\green{\boxed{ \bf \:Time = \dfrac{Distance}{Speed} }}$

So,

Time taken to travel 'x' km at a speed of 5 km per hour is

$\purple{\rm :\longmapsto\:t_1 = \dfrac{x}{5} - - - (1)}$

Case :- 2

We have

• Distance covered on bicycle = x km

• Speed during this = 10 km per hour

So,

Time taken to travel '(20 - x)' km at a speed of 10 km per hour is

$\purple{\rm :\longmapsto\:t_2 \: = \: \dfrac{20 - x}{10} - - - (2)}$

According to statement,

Total time taken to covered 20 km = 2hours

$\bf :\longmapsto\:t_1 + t_2 = 2$

$\rm :\longmapsto\:\dfrac{x}{5} + \dfrac{20 - x}{10} = 2$

$\rm :\longmapsto\:\dfrac{2x + 20 - x}{10} = 2$

$\rm :\longmapsto\:\dfrac{x + 20 }{10} = 2$

$\rm :\longmapsto\:x + 20 = 20$

$\bf\implies \:x = 0$

$\bf\implies \:Distance \: covered \: by \: foot = 0 \: km$

Additional Information :-

$\green{\boxed{ \bf \:Speed= \dfrac{Distance}{Time} }}$

$\green{\boxed{ \bf \:Distance = Speed \times Time}}$