A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

byAmlesh Mahato •October 11, 2020

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Solution:

⇨Let the initial speed of train be u km/h

⇨Therefore time required to travel 480 km is

$\large t=\frac{d}{v}$

$\large \Rightarrow t=\frac{480}{u}$ sec

⇨Now V=u-8 km/h

⇨And t=t+3

Again,

$\large d=vt$

$\large \Rightarrow 480=(u-8)t$

$\large \Rightarrow 480=(u-8)(\frac{480}{u}+3)$

$\large \Rightarrow 480=(u-8)(\frac{480+3u}{u})$

$\large \Rightarrow 480u=(u-8)(480+3u)$

$\large \Rightarrow 480u=480u+3u^2-3840-24u$

$\large \Rightarrow 480u-480u=3u^2-3840-24u$

$\large \Rightarrow 3u^2-24u-3840=0$

$\large \Rightarrow u^2-8u-1280=0$

⇨From the above quadratic equation we can find speed of the train.

Exercise 4.1

1. Check whether the following are quadratic equations :

(i) $\large (x + 1)^2=2(x-3)$

(ii) $\large x^2-2x=(-2)(3-x)$

(iii) (x – 2)(x + 1) = (x – 1)(x + 3)

(iv) (x – 3)(2x +1) = x(x + 5)

(v) (2x – 1)(x – 3) = (x + 5)(x – 1)

(vi) $\large x^2+3x+1=(x-2)^2$

(vii) $\large (x+2)^3=2x(x^2-1)$

(viii) $\large x^3-4x^2-x+1=(x-2)^3$

2. Represent the following situations in the form of quadratic equations :

(i) The area of a rectangular plot is 528 m2 . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been8 km/h less, then it would have taken 3 hours more to cover the same distance. Weneed to find the speed of the train.

Tags: Chapter-4 Exercise-4.1 Math- Class 10