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# a train travels 360 km at a uniform speed if the speed had been 5 km more

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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. 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.

Solving a Quadratic Equation by Factorization Method

A train trave... Question

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.

Open in App Solution Given, Distance = 360 km Let the speed be x , then time taken t = 360 x

If speed is increased by 5 km/h speed will be

( x + 5 ) km/h

Distance is the same

t = 360 ( x + 5 )

time with original speed - time with increased speed

= 1 therefore, 360 x − 360 ( x + 5 ) = 1 L C M = x ( x + 5 ) Hence, 360 ( x + 5 ) − 360 x x ( x + 5 ) = 1 360 x + 1800 − 360 x = x ( x + 5 ) x 2 + 5 x = 1800 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 k m h r ,

So the speed of the train is 40 km/hr. We have discarded the other value as the negative value of speed

( − 45 ) is not possible. Suggest Corrections 132

SIMILAR QUESTIONS

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

360 k m

at a uniform speed. If the speed had been

5 k m / h

more, it would have been taken

1

hours less for the same journey. Find the speed of the train.

Q.

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​​

Q.

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.

Click here👆to get an answer to your 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.

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.

Medium Open in App

Updated on : 2022-09-05

Given distance=360 km.

Solution Verified by Toppr

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

Speed when increased by 5 km/hr =(x+5) km/hr

x 360 ​ − (x+5) 360 ​ =1 x(x+5) [360x+1800−360x] ​ =1 x 2 +5x−1800=0 x 2 +45x−40x−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.

Video Explanation

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## Ex 4.3, 8

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/𝑥 " – 1" ) = 360 (x + 5) ((360 − 𝑥)/

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## Ex 4.3, 8 - Chapter 4 Class 10 Quadratic Equations (Term 2)

Last updated at March 16, 2023 by Teachoo

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### Transcript

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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