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.​

Answer 1

S O L U T I O N :

Let,

• The speed of the train be R km/hr.

• Time taken to cover 360 km = 360/R hr.

According to the question,

⇒ (R + 5)(360-1/R) = 360

⇒ 360 - R + 1800-5/R= 360

⇒ R² + 5R + 10R - 1800 = 0

⇒ R(R + 45) - 40(R + 45) = 0

⇒ (R + 45) (R - 40) = 0

⇒ R = 40, -45

[ Note :- Ignoring negative term ]

⇒ R = 40 km/h

Therefore,

• The speed of the train is 40 km/h.

Answer 2

$\huge{\boxed{\rm{Question}}}$

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.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• 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.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• The speed of the train.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• The speed of the train =

$\large{\boxed{\boxed{\sf{Assumptions}}}}$

• The speed of the train be x km/h.

• Time taken to cover 360 km = 360/x km/h.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that there is a train that is moving on a uniform speed of 360 km. Afterthat it says that if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Now, it ask us to find the speed of the train.

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Procedure \: of \: the \: question \: is \: given \: below}}}}$

• To solve this question firstly we have to take assumptions as we already taked. Now we have to put the values after that we get our final results.

$\large{\boxed{\boxed{\sf{Full \: solutions}}}}$

• (x+5) (360-1/x) = 360

• 360 - x + 1800 -5/x = 360

• x² + 5x + 10x - 1800 = 0

• x(x+45) - 40(x+45) = 0

• (x+45) (x+40) = 0

• x = 40 , - 45

• x = 40 km/h

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