Question

꧁A train covers a distance 480km at uniform speed.if speed had been 8km/hr less then it would have taken 3hours more to covers the same distance.find the visual speed of the train.࿐

Answer 1

Given :

• A train covers a distance 480km at uniform speed.if speed had been 8km/hr less then it would have taken 3hours more to covers the same distance.

To Find :

• Speed of train = ?

Solution :

Let speed of train be x

As we know that,

• Time = Distance ÷ speed

Now,

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

$:\implies \sf \dfrac{480}{x} = \dfrac{480}{x - 8} + 3$

$:\implies \sf \dfrac{480}{x} - \dfrac{480}{x - 8} = 3$

$:\implies \sf {3x}^{2} - 24x + 3840 = 0$

$:\implies \sf 3( {x}^{2} - 8x + 1280) = 0$

$:\implies \sf {x}^{2} - 8x + 1280 = 0$

$:\implies \sf {x}^{2} - 40x + 32x + 1280 = 0$

$:\implies \sf x(x - 40) + 32(x-40)= 0$

$:\implies \sf (x + 32) (x-40)= 0$

$:\implies \sf x = 40 \: or \: x = - 32$

As we know that, we can't calculate speed in negative. So, x = 40

$:\implies \underline{ \boxed{ \sf x = 40 \: km/hr}}$

$\therefore\:\underline{\textsf{The speed of train is \textbf{40 km/hr}}}.$

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