Question

A train travel 360km at uniform speed. If the speed had been 5km/hrs more, if it would have taken 1hrs less the same journey from the quadratic equation to find the speed of the train

Answer 1

Step-by-step explanation:

Let the speed of the train be x km/h.Distance covered by the train = 360 km

1st case- Time, T1 = distance / speed1 = 360 / x

2nd case- Time, T2 = distance / speed2 = 360 / x + 5

According to the question,

360 / x - 1 = 360 / x + 5(or) 360 / x - 360 / x + 5 = 1

360 (x+5) -360 (x) / x (x+5) =1

360x + 1800 - 360x / x2 + 5x = 1

1800 = x2 + 5x

x2 + 5x - 1800 =0

Answer 2

Given : -

A train travel 360km at uniform speed. If the speed had been 5km/hrs more, if it would have taken 1hrs less the same journey

Required to find : -

• Speed of the train ?

Solution : -

A train travel 360km at uniform speed. If the speed had been 5km/hrs more, if it would have taken 1hrs less the same journey

we need to find the speed of the train ?

So,

From the given data we can consider that ;

Let the speed of the train be " x " km/hr .

Total journey/ distance = 360 km

Here, we have 2 cases ;

1st case : -

Let the speed of the train be x km/hr

Distance = 360 km

we know that ;

Time = Distance/Speed

So,

Time taken to cover this distance = 360/x

Similarly,

Case - 2 : -

Distance = 360 km

It is mentioned that ;

Speed of the train had been increased by 5 km/hr .

So,

Let the speed of the train be x + 5 km/hr

This implies ;

Time taken to cover this distance = 360/x + 5

However,

It is also given that ;

If the speed had been 5km/hrs more, if it would have taken 1hrs less the same journey

So,

According to the problem ;

➜ 360/x - 1 = 360/x + 5

This implies ;

➜ 360/x - 360/x + 5 = 1

Let's solve this further ;

➜ x + 5 ( 360 ) - x ( 360 )/ x ( x + 5 ) = 1

➜ x + 5 ( 360 ) - 360x = x² + 5x

➜ 360x + 1800 - 360x = x² + 5x

➜ ( 360x , - 360x get's cancelled due to opposite signs )

➜ 1800 = x² + 5x

➜ 0 = x² + 5x - 1800

➜ x² + 5x - 1800

Hence,

The quadratic equation for the given scenario is x² + 5x - 1800

Now,

Let's solve this Quadratic equation to find the speed of the train .

➜ x² + 5x - 1800

➜ x² + 45x - 40x - 1800 = 0

➜ x ( x + 45 ) - 40 ( x + 45 ) = 0

➜ ( x + 45 ) ( x - 40 ) = 0

This implies ;

x + 45 = 0

x = - 45

___________

x - 40 = 0

x = 40

Since,

The speed of the train can't be in negative .

Therefore,

Speed of the train = x = 40 km/hr

Additional Information : -

Quadratic formula :-

$\boxed{\sf{ x = \dfrac{- b \pm \sqrt{ b^2 - 4ac }}{2a } }}$

Here,

b² - 4ac is called to be or known to be as Discriminate .

This is because ,

This helps us to find the nature of the roots .

The discriminate is denoted by letter " D "

The conditions are ;

• If D > 0

The roots are real and distinct ( different ) .

• If D = 0

The roots are equal and real .

• If D < 0

The roots are imaginary .