# 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.

Byju's Answer Standard X Mathematics

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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Standard X Mathematics

## 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.

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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)/

**Check sibling questions**

## 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

**Next**: Ex 4.3, 9 Important →

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### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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