Question

A trai cover a distance of 360 km at uniform speed. if its speed is increased by 5km/hr then it would take 1hour less. find the speed of the train​

Answer 1

Answer:

• The original speed of train is 40 km/hr.

Step-by-step explanation:

Given that:

• A train cover a distance of 360 km at uniform speed.
• Its speed is increased by 5 km/hr then it would take 1 hour less.

To Find:

• The original speed of train.

Formula used:

• Time = Distance/Speed

Let us assume:

• The original speed of train be x km/hr.
• Original Time = 360/x

When speed is increased:

• New speed = (x + 5) km/hr
• New time = 360/(x + 5)

Finding the original speed of train:

According to the question.

⟶ 360/x = 360/(x + 5) + 1

⟶ 360/x - 360/(x + 5) = 1

Taking 360 common in LHS.

⟶ 360{1/x - 1/(x + 5)} = 1

⟶ 1/x - 1/(x + 5) = 1/360

Taking x(x + 5) common in LHS.

⟶ (x + 5 - x)/{x(x + 5)} = 1/360

Cross multiplication.

⟶ 5 × 360 = x(x + 5)

⟶ 1800 = x² + 5x

⟶ x² + 5x - 1800

Splitting 5x into 45x and - 40x.

⟶ x² + 45x - 40x - 1800 = 0

⟶ x(x + 45) - 40(x + 45) = 0

⟶ (x - 40) (x + 45) = 0

⟶ x = 40 or x = - 45

⟶ x = 40 [Because speed is always positive]

∴ The original speed of train = 40 km/hr

Answer 2

Answer:

Given :-

• A train cover a distance of 360 km at uniform speed.
• The speed is increased by 5 km/hr then it would take 1 hour less.

To Find :-

• What is the speed of the train.

Solution :-

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

$\mapsto$ Speed when increased by 5 km/h then,

$\implies$ $\sf\bold{\pink{(x + 5)\: km/hr}}$

According to the question :

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

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

$\implies \sf \dfrac{\cancel{360x} + 1800 \cancel{- 360x}}{{x}^{2} + 5x} =\: 1$

By doing cross multiplication we get,

$\implies \sf {x}^{2} + 5x =\: 1800$

$\implies \sf {x}^{2} + 5x - 1800 =\: 0$

$\implies \sf {x}^{2} + (45 - 40)x - 1800 =\: 0$

$\implies \sf {x}^{2} + 45x - 40x - 1800 =\: 0$

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

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

$\implies \sf (x + 45) =\: 0$

$\implies \sf\bold{\purple{x =\: - 45}}$

Either,

$\implies \sf (x - 40) =\: 0$

$\implies \sf\bold{\red{x =\: 40}}$

Since, we can't take speed as negetive (- ve).

So, x = 40

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