Question

Q.8 A train covers a distance of 480 km at a uniform speed. If the speed had been 8
km/hr lessthan it would have taken 3 hours more to cover the same distance.
Find the usual speed of the train.​

Answer 1

Let the speed of train be x km/hr.

$\Rightarrow$ Distance travelled by train = 480 km

Speed of train = $\sf{\frac{480}{x}}$ km/hr

If speed is decreased by 8 km/hr. Then,

Speed of train = $\sf{\frac{480}{x\:-\:8}}$ km/hr

If the speed had been 8 km/hr lessthan it would have taken 3 hours more to cover the same distance.

According to question,

=> $\sf{\frac{480}{x\:-\:8}}$ - $\sf{\frac{480}{x}\:=\:3}$

=> $\sf{\frac{480(x)\:-\:480(x\:-\:8)}{x(x\:-\:8)}\:=\:3}$

=> $\sf{\frac{480x\:-\:480x\:+\:3840}{x^2\:-\:8x}\:=\:3}$

=> $\sf{\frac{3840}{3}\:=\:x^2\:-\:8x}$

=> $\sf{1280\:=\:x^2\:-\:8x}$

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

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

=> $\sf{x(x\:-\:40)\:+32(x\:-\:40)\:=\:0}$

=> $\sf{(x\:-\:40)\:(x\:+\:32)\:=\:0}$

=> $\sf{x\:=\:40}$

(-32 neglected, as speed can't be negative)

•°• Speed of train is 40 km/hr.

Answer 2

$\huge{\mathfrak{\underline{\underline{\red{Answer:}}}}}$

$\star{\bf{\underline{Given:}}}$

• Distance covered by train = 480 km.

Now, let the speed of train be 'x km/h'.

$\sf{\implies Speed\;of\;train=\dfrac{480}{x}km/h}$

Now, speed is decreased by 8 km/h.

$\sf{Now,\;speed\;of\;train=\dfrac{480}{x-8}km/h}$

Now, according to question.

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

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

$\sf{\implies \dfrac{480}{3}\times 8=x^{2}-8x}$

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

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

$\sf{\underline{Now,\;we\;will\;solve\;it\;by\;splitting\;middle\;term\;method.}}$

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

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

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

$\sf{\underline{We\;neglect\;-32\;because\;speed\;cannot\;be\;negative.}}$

$\implies {\large{\red{\bf{x=40\;km/h}}}}$

$\large{\red{\bf{Hence,\;Speed\;of\;train\;be\;40\;km/h.}}}$