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

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Detailed Solution

Let the uniform speed of the train be x km/h. The train travels 360 km at that uniform speed.

time = \frac{distance}{time}

Now, the train when it’s traveling 360 km with a speed of x km/h. let it be t hour.
So, the time required is

t = \frac{360}{x}

Now, If the speed had been (x+5) km/h, it would have taken 1 hr less which is (t−1) hour for the same journey.
Now, time t−1=

\frac{360}{x + 5}

We have two equations of two unknowns.
t−1=

\frac{360}{x + 5}

⇒

\frac{360}{x}

−1=

\frac{360}{x + 5}

⇒

\frac{360}{x}

\frac{360}{x + 5}

= 1
We get the quadratic form and get 360(x+5)−360x=x(x+5).
The equation becomes x2+5x−1800=0.
x2+5x−1800=0
⇒ x2+45x−40x−1800=0
⇒(x+45)x−40(x+45)=0
⇒(x+45)(x−40)=0
The solution of the factorization is x=40. It can’t be -45 as it’s velocity.
Therefore, the speed of the train is 40 km/h.

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