Question

Aman riding a cycle covers a distance of 60 km in the direction of wind and comes back to the original place in 8 hours. If the speed of the wind is 10 km/hr, find the speed of the bicycle.

Answer 1

Answer:

80 km

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Answer 2

$\huge\sf\pink{Answer}$

☞ Cycle's speed = 20km/h

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$\huge\sf\blue{Given}$

✭ Aman rides a bicycle and covers a distance of 60 km in the direction of wind

✭ He comes back to the original place in 8 hours

✭ Speed of wind = 10 km/h

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$\huge\sf\gray{To \:Find}$

◈ Speed of cycle?

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$\huge\sf\purple{Steps}$

So here,

➢ Speed of Aman = x km/h

➢ Distance covered in one direction = d = 60km

➢ Speed of the wind = 10 km/hr

➢ Total time taken = 8 hr

If he rides with the speed of wind,

➝ $\sf Relative \ speed = s_1 = (x+10) km/h$

➝ $\sf D = 60 \ km$

➝ $\sf t_1 = \dfrac{d}{s_1}$

➝ $\sf t_1= \dfrac{60}{(x+10)} \:\:\: -eq(1)$

If he rides opposite to wind,

➳ $\sf Relative \ speed = s_2= (x-10) km/h$

➳ $\sf D= 60 \ km$

➳ $\sf t_2 = \dfrac{60}{(x-10)} hr\:\:\: -eq(2)$

So we know that,

»» $\sf t_1+t_2 =8 \ hr$

»» $\sf \dfrac{60}{(x+10)}+ \dfrac{60}{(x-10)} = 8$

»» $\sf 60\bigg(\dfrac{1}{(x+10)} + \dfrac{1}{(x-10)}\bigg)= 8$

»» $\sf 60 \bigg(\dfrac{(x-10+x+10)}{(x^2 - 10^2)}\bigg)= 8$

»» $\sf 60(2x) = 8(x^2-100)$

»» $\sf \dfrac{120x}{8} = x^2-100$

»» $\sf 15x = x^2-100$

»» $\sf x^2-15x-100=0$

»» $\sf x^2 -20x+5x -100=0$

»» $\sf x(x-20)+5(x-20)=0$

»» $\sf (x-20)(x+5) =0$

»» $\sf x-20 =0 or x+5=0$

»» $\sf x=20 or x= -5$ « Ignoring Negatively »

»» $\sf\orange{ x= 20}$

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