Represent the following situations in the form of quadratic equations. A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less - Mathematics

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Sum

Represent the following situation in the form of a quadratic equation.

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.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. 

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Solution

Let the speed of the train be x km/h.
Time taken to travel 480 km = 480/x km/h
In second condition, let the speed of train = (x - 8) km/h
It is also given that the train will take 3 hours to cover the same distance.

`480/x`

`480/(x - 8)`

`480/(x - 8) = 480/x + 3`

`480/(x - 8) - 480/x = 3`

`((480)(8))/((x - 8)(x)) = 3`

x2 - 8x - 1280 = 0

ax2 + bx + c = 0

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

x = `(8 ± sqrt(64 + 4(1280)))/2`

= `(8 ± 72)/2`

= 40 km/hr

  Is there an error in this question or solution?
Chapter 4: Quadratic Equations - Exercise 4.1 [Page 74]

APPEARS IN

NCERT Mathematics Class 10
Chapter 4 Quadratic Equations
Exercise 4.1 | Q 2.4 | Page 74
RS Aggarwal Secondary School Class 10 Maths
Chapter 10 Quadratic Equations
Exercises 5 | Q 45

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