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Answer 1

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

Step-by-step explanation:

Let the uniform speed of the train be x km/h.

Then time taken to cover 360 km=$\frac{360}{x}h$

Now, new increased speed=(x+5) km/h

So, time taken to cover 360 km=$\frac{360}{x+5}h$

According to the question,

$\frac{360}{x}-\frac{360}{x+5}=1\\ \\ 360(\frac{1}{x}-\frac{1}{x+5})=1\\ \\ \frac{360(x+5-x)}{x(x+5)}=1\\ \\ \implies \frac{360\times 5}{x(x+5)}=1\\ \\ \implies 1800=x^2+5x\\ \therefore x^2+5x-1800=0\\ \implies x^2+45x-40x-1800=0\\ \implies x(x+45) -40(x+5)=0\\ \implies (x+5) (x-40)=0\\ \therefore x=-45, 40 \\ \rm But\ speed\ can't\ be\ nagative,\ so\ x\neq-45\\ \therefore x=40\\ \rm The\ uniform\ speed\ of\ the\ train\ is\ 40\ km/h$