Question

8. 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

Answer:

Speed of the train is 40 km/hr.

Step-by-step explanation:

Given:

A train travels 360 km at uniform speed.

If the speed has been 5 km/hr moe, 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/hr.

When speed is increased by 5 km/hr then (x + 5) km/hr.

$\dashrightarrow \sf \dfrac{360}{x} - \dfrac{360}{(x + 5)} = 1$

$\dashrightarrow \sf \dfrac{360x + 1800 - 360x}{x (x + 5)} = 1$

$\dashrightarrow \sf x^2 + 5x - 1800 = 0$

$\dashrightarrow \sf x^2 + 45x - 40x - 1800 = 0$

$\dashrightarrow \sf x(x+45) - 40(x+45) = 0$

$\dashrightarrow \sf (x-40)(x+45) = 0$

$\dashrightarrow \sf x = 40, \ x = 45$

$\therefore$ Speed of the train is 40 km/hr.

Answer 2

Answer :

• Speed of the train is 40km/hr

Given :

• A train travels 360 km at a uniform speed
• The speed had been 5 km/h more it would have taken 1 hour less for the same journey

To find :

• Speed of the train.

Solution :

• Let the speed of the train be x km/hr

First we need to find the time ,

Given,

• Distance is 360km
• Speed = x km/hr

As we know that,

• Speed = Distance/Time

》Speed = 360/Time

》Time = 360/x

Time = 360/x

Given,

• Speed = x + 5 km/hr
• Distance = 360km
• Time = 360/x - 1

We know that,

• Speed = Distance/Time

》x + 5 = 360 / (360/x -1)

》(x + 5) = (360/x - 1 )= 360

》(x + 5) = (360/x - x )= 360

》(x + 5) = (360 - x) = 360x

》x(360 - x) - 5(x - 360) = 360x

》360x - x² + 5(360) - 5x = 360x

》360x - x² + 1800 - 5x - 360x = 0

》- x² - 5x - 360 × 360x + 1800 = 0

》-x² - 5x + 1800 = 0

》x² + 45x - 40x - 1800 = 0

》x(x + 45) - 40(x + 45) = 0

》(x + 45) (x - 40) = 0

》x + 45 = 0 or x - 40 = 0

》x = -45 or x = 40

We know that,

• Speed of train is x so , x can't be negative

Hence , Speed of the train is 40km/hr