# 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

Sum

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, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

#### 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.
Therefore, time taken to travel 480 km = (480/x + 3)
Speed × Time = Distance

⇒ (x - 8)(480/x + 3) = 480

⇒ 480 + 3x - 3840/x - 24 = 480

⇒ 3x - 3840/x = 24

⇒ 3x2 - 24x - 3840 = 0

⇒ 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 Class 10 Maths