Question

A train travels 360 km at a uniform speed if speed had been 5 km /h more it would have taken hours less for the same journey find the speed of the train

Answer 1

Answer:

40 Km/hr

Step-by-step explanation:

Consider the given question,

Distance =360 km

Speed =x km/hr

When speed is increase (x+5) km/hr

Given expression is written as,

⇒  360 x − (x+5) 360

​  =1

⇒  x(x+5) x+5−x

​  =  360 1

​  ⇒  2 x+5x=1800

⇒  2 x +5x−1800=0

⇒2x 2 +45x−40x−1800=0

⇒x(x+45)−40(x+45)=0

⇒(x+45)(x−40)=0

⇒x=40,−45

But, speed can not be negative.

Hence, speed is 40 km/hr

Hope this helps

Answer 2

Correct Question :-

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.

Given :-

• A train travels 360 km at a uniform speed.

• If speed had been 5 km/h more it would have taken 1 hour less for the same journey.

To find :-

• The speed of the train

Solution :-

Let the speed of the train be x km/h

Distance = 360 km

Time = distance/speed = 360/x h

Again,

If the speed had been 5 km/h more then,

Distance = 360 km

Time = distance/speed = 360/x+5 h

Now,

❇️ According to the question,

$\rm\:\dfrac{360}{x}=\dfrac{360}{x+5}+1$

$\rm\longrightarrow\:\dfrac{360}{x}-\dfrac{360}{x+5}=1$

$\rm\longrightarrow\:\dfrac{360(x+5)-360x}{x(x+5)}=1$

$\rm\longrightarrow\:\dfrac{360x+1800-360x}{{x}^{2}+5x}=1$

$\rm\longrightarrow\:\dfrac{1800}{{x}^{2}+5x}=1$

$\rm\longrightarrow\:1800=1\times\:({x}^{2}+5x)$

$\rm\longrightarrow\:1800={x}^{2}+5x$

$\rm\longrightarrow\:{x}^{2}+5x-1800=0$

$\rm\longrightarrow\:{x}^{2}+45x-40x-1800=0$

$\rm\longrightarrow\:x(x+45)-40(x+45)=0$

$\bf\longrightarrow\:(x+45)(x-40)=0$

Now,

$\rm\:x+45=0$

$\rm\longrightarrow\:x=0-45$

$\bf\longrightarrow\:x=-45$

Then,

$\rm\:x-40=0$

$\rm\longrightarrow\:x=0+40$

$\bf\longrightarrow\:x=40$

We know that speed cannot be negative.Hence, the speed of the train will be 40 km/h.