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Home » 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
CBSE | Class 10 | Exercise 4.3 | Quadratic Equations
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

Solution:

Let us say, the speed of the train be x km/hr.

Time taken to cover 360 km = 360/x hr.

As per the question given,

\Rightarrow \left( x~+\text{ }5 \right)\left( 360-1/x \right)\text{ }=\text{ }360

\Rightarrow 360\text{ }~x~+\text{ }1800-5/x~=\text{ }360

\Rightarrow ~{{x}^{2~}}+~5x~+\text{ }10x~\text{ }1800\text{ }=\text{ }0

\Rightarrow ~x\left( x~+\text{ }45 \right)\text{ }-40\left( x~+\text{ }45 \right)\text{ }=\text{ }0

\Rightarrow \left( x~+\text{ }45 \right)\left( x~\text{ }40 \right)\text{ }=\text{ }0

\Rightarrow ~x~=\text{ }40,\text{ }-45

As we know, the value of speed cannot be negative.

Therefore, the speed of train is 40 km/h.

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