A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train ?

byAmlesh Mahato •March 10, 2022

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Solution:

⇒ Let the Speed of the train = x km/h

⇒ Let Time taken to cover 360 km = t1

Given

⇒ Distance: 360 km

A/Q

⇒ Time required to cover 360 km

$A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train ?$

$A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train ?$

⇒ If Velocity = ( x + 5 ) Km/h

⇒ Then t2 = ( t1 - 1 ) hour

Now

$\Rightarrow d=vt_{2}$

$A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train ?$

$\Rightarrow 360=\left ( x+5 \right )\left ( \frac{360}{x}-1 \right )$

$\Rightarrow 360=\left ( x+5 \right )\left ( \frac{360-x}{x} \right )$

$\Rightarrow 360x=\left ( x+5 \right )\left ( {360-x} \right )$

$\Rightarrow 360x=360x-x^{2}+1800-5x$

$\Rightarrow x^{2}+5x-1800=0$

$\Rightarrow x^{2}+2\times x \times \frac{5}{2}+\left ( \frac{5}{2} \right )^{2}-\left ( \frac{5}{2} \right )^{2}-1800=0$

$\Rightarrow \left ( x+\frac{5}{2} \right )^{2}=\left ( \frac{5}{2} \right )^{2}+1800$

$\Rightarrow \left ( x+\frac{5}{2} \right )^{2}=\frac{25}{4}+1800$

$\Rightarrow \left ( x+\frac{5}{2} \right )^{2}=\frac{25+7200}{4}$

$\Rightarrow \left ( x+\frac{5}{2} \right )^{2}=\frac{7225}{4}$

$\Rightarrow \left ( x+\frac{5}{2} \right )^{2}=\left ( \frac{85}{2} \right )^{2}$

$\Rightarrow x+\frac{5}{2}=\pm \frac{85}{2}$

$\Rightarrow x=-\frac{5}{2}\pm \frac{85}{2}$

$\Rightarrow x=-\frac{5}{2}+ \frac{85}{2},-\frac{5}{2}- \frac{85}{2}$ $\Rightarrow x=\frac{-5+85}{2},\frac{-5-85}{2}$

$\Rightarrow x=\frac{80}{2},\frac{-90}{2}$

$\Rightarrow x=40,-45$

⇒ Speed can't be negative, so speed of the train is 40 km/h

Tags: Exercise-4.3 Math- Class 10 Mathematics