train travel 360 km at a uniform speed

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Question 8 - Ex 4.3 - Chapter 4 Class 10 Quadratic Equations

Last updated at April 16, 2024 by Teachoo

Ex 4.3 ,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. Let the speed of train be x km/hr From (1) (x + 5) (360/ " 1" ) = 360 (x + 5) ((360 )/ ) = 360 (x + 5) (360 x ) = 360x x(360 x) + 5(360 x ) = 360 x 360x x2 +5(360) 5x = 360 x 360x x2 + 1800 5x = 360 x 360x x2 + 1800 5x 360 x = 0 x2 5x 360 x + 360x + 1800 = 0 x2 5x + 1800 = 0 0 = x2 + 5x 1800 x2 + 5x 1800 = 0 We factorize by splitting the middle term method x2 + 45x 40x 1800 = 0 x (x + 45) 40 (x + 45) = 0 (x + 45) (x 40) = 0 Hence x = 45, x = 40 are the roots of the equation We know that Speed of train = x So, x cannot be negative x = 40 is the solution So, Speed of train = x = 40 km/hr

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A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train

Let the speed of the train be s km/hr and the time taken be t hours.

Distance = Speed × Time

360 = s × t

⇒ t = 360 / s

Increased speed of the train can be written as s + 5

New time to cover the same distance = t - 1

(s + 5) × (t - 1) = 360 ....(1)

st - s + 5t - 5 = 360

360 - s + 5(360/s) - 5 = 360 [Since, st = 360 and t = 360 / s]

- s + 1800/s - 5 = 0

- s² + 1800 - 5s = 0

s² + 5s - 1800 = 0

We will solve this quadratic equation by quadratic formula

Comparing s² + 5s - 1800 = 0 with ax 2  + bx + c = 0, we get a = 1, b = 5, c = - 1800

b² - 4ac = (5) 2  - 4(1)(- 1800)

= 25 + 7200

= 7225 > 0

Hence, the real roots exist.

x = [-b ± √ (b 2  - 4ac)] / 2a

s = (- 5 ± √ 7225) / 2

s = (- 5 ± 85) / 2

s = (- 5 + 85) / 2 and s = (- 5 - 85) / 2

s = 80 / 2 and s = - 90 / 2

s = 40 and s = - 45

Speed of the train cannot be a negative value.

Therefore, speed of the train is 40 km /hr.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 4

Video Solution:

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Find the speed of the train

Class 10 Maths NCERT Solutions  Chapter 4 Exercise 4.3 Question 8

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey, then the speed of the train is 40 km/hr.

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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.

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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.

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey.

We have to find the original speed of the train.  

Let the original speed of the train be $x$ km/hr.

This implies,

Time taken by the train to travel 360 km at original speed$=\frac{360}{x}$ hours

Time taken by the train to travel 360 km when the speed is 5 km/hr more than the original speed$=\frac{360}{x+5}$ hours

According to the question,

$\frac{360}{x}-\frac{360}{x+5}=1$

$\frac{360(x+5)-360(x)}{(x)(x+5)}=1$

$\frac{360(x+5-x)}{x^2+5x}=1$

$(360)(5)=1(x^2+5x)$   (On cross multiplication)

$1800=x^2+5x$

$x^2+5x-1800=0$

Solving for $x$ by factorization method, we get,

$x^2+45x-40x-1800=0$

$x(x+45)-40(x+45)=0$

$(x+45)(x-40)=0$

$x+45=0$ or $x-40=0$

$x=-45$ or $x=40$

Speed cannot be negative. Therefore, the value of $x$ is $40$ km/hr.

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

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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 distance = 360 km. let the speed of the train be x km/hr. speed when increased by 5 km/hr = ( x + 5 ) km/hr 360 x − 360 ( x + 5 ) = 1 [ 360 x + 1800 − 360 x ] x ( x + 5 ) = 1 x 2 + 5 x − 1800 = 0 x 2 + 45 x − 40 x − 1800 = 0 x ( x + 45 ) − 40 ( x + 45 ) = 0 ( x − 40 ) ( x + 45 ) = 0 x = 40 , − 45 the speed of the train is 40 km/hr..

A train travels 360 km at a uniform speed if the speed had been 5 km more it would have taken 1 hour less from the same journey find the speed of the train​​

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

Let us assume that the speed of the train be ‘x ’ km/hr. we are also given that the distance covered during the journey is 360 km. now, time taken during the journey = hr time taken for the new journey = hr according to the question, hence, this is the required quadratic equation..

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

A train travels 360 km at a uniform speed if the speed had been 5 km more it would have taken 1 hour less from the same journey find the speed of the train​​