Question

a bike Travels 400 kilometre at usual speed if the speed had been 5 km per hour less it would have taken 4 hours more for the same journey find speed of the bike​

Answer 1

Answer:

speed=25, 20

Step-by-step explanation:

this is your answer

Answer 2

Answer :-

Speed of the bike is 25 Km / h.

Explanation :-

Distance traveled by bike ( d ) = 400 Km

Let the speed ( s₁ ) of the bike be 'x' Km / h

Time taken to travel ( t₁ ) = d / s₁ = ( 400 / x ) hours

[ ∵ Speed = Distance / Time ]

If the speed of the bike is reduced by 5 Km / h

Speed of the bike ( s₂ ) = ( x - 5 ) Km / h

Distance traveled by bike ( d ) = 400 Km

Time taken to travel ( t₂ ) = [ 400 / ( x - 5 ) ] Hours

Given

If the speed of the bike is reduced by 5 Km / h it would take 4 hours more to complete the same journey

So, t₂ = t₁ + 4

$\implies \dfrac{400}{x - 5} = \dfrac{400}{x} + 4 \\ \\ \\ \implies \dfrac{400}{x - 5} - \dfrac{400}{x} = 4 \\ \\ \\ \implies \dfrac{400(x) - 400(x - 5)}{x(x - 5)} = 4 \\ \\ \\ \implies \dfrac{400x - 400x + 2000}{ {x}^{2} - 5x} = 4 \\ \\ \\ \implies \dfrac{2000}{ {x}^{2} - 5x} = 4$

$\implies \dfrac{500}{x ^{2} - 5x} = 1 \\ \\ \\ \implies {x}^{2} - 5x = 500 \\ \\ \\ \implies {x}^{2} - 5x - 500 = 0 \\ \\ \\ \implies {x}^{2} - 25x + 20x - 500 = 0 \\ \\ \\ \implies x(x - 25) + 20(x - 25) = 0 \\ \\ \\ \implies (x - 25)(x - 20) = 0$

$\implies x - 25 = 0 \ \ or \ \ x + 20 = 0 \\ \\ \\ \implies x = 25 \ \ or \ \ x = - 20 \\ \\ \\ \textsf{as speed cannot be negative} \\ \\ \\ \implies x = 25$

∴ the speed of the bike is 25 Km / h.