Ex 4.1, 2 (iv) - Chapter 4 Class 10 Quadratic Equations

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 4.1, 2
Represent the following situations in the form of quadratic equations :
(iv) 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.
Let Speed of train be x km/hr
Normal speed
Distance = 480 km
Speed = x km/hr
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x = 480/𝑇𝑖𝑚𝑒
Time = 𝟒𝟖𝟎/𝒙
Speed became 8 km/h less
Distance = 480 km
Speed = (x – 8) km/hr
Time = 480/𝑥 + 3
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x – 8 = 480/((480/𝑥 " + 3" ) )
(x – 8) (𝟒𝟖𝟎/𝒙 " + 3" ) = 480
From (1)
(x – 8) (𝟒𝟖𝟎/𝒙 " + 3" ) = 480
(x – 8) ( (480 + 3𝑥)/𝑥) = 480
(x – 8) (480 + 3x) = 480 x
x (480 + 3x) – 8 (480 + 3x) = 480 x
480x + 3x2 – 3840 – 24x = 480 x
480x + 3x2 – 384 – 24x – 480 x = 0
3x2 + 480x – 480x – 24x 3840 = 0
3x2 – 24x – 3840 = 0
3 (x2 – 8x – 1280) = 0
x2 – 8x – 1280 = 0/3
x2 – 8x – 1280 = 0
It is the form of ax2 + bx + c = 0
Where a = 1, b = – 8 , c = –1280
Hence, it is a quadratic equation .

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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