AskSia

Plus

A train travels a distance of 480 km at a uniform speed if the speed had been 8 ...

Jul 21, 2024

A train travels a distance of 480 km at a uniform speed if the speed had been 8 km per hour less then it would have taken 3 hours more to cover same distance we need to find speed of the train

Generated Graph

Solution by Steps

step 1

Let the speed of the train be

x

km/h

step 2

The time taken to travel 480 km at

x

km/h is

\frac{480}{x}

hours

step 3

If the speed is 8 km/h less, the speed is

(x - 8)

km/h

step 4

The time taken to travel 480 km at

(x - 8)

km/h is

\frac{480}{x - 8}

hours

step 5

According to the problem, the difference in time is 3 hours:

\frac{480}{x - 8} - \frac{480}{x} = 3

step 6

Multiply both sides by

x(x - 8)

to clear the denominators:

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

step 7

Simplify the equation:

480x - 480x + 3840 = 3x^2 - 24x

step 8

Combine like terms:

3840 = 3x^2 - 24x

step 9

Rearrange the equation:

3x^2 - 24x - 3840 = 0

step 10

Divide the entire equation by 3:

x^2 - 8x - 1280 = 0

step 11

Solve the quadratic equation using the quadratic formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

, where

a = 1

b = -8

, and

c = -1280

step 12

Calculate the discriminant:

b^2 - 4ac = (-8)^2 - 4(1)(-1280) = 64 + 5120 = 5184

step 13

Find the roots:

x = \frac{8 \pm \sqrt{5184}}{2} = \frac{8 \pm 72}{2}

step 14

The solutions are

x = \frac{80}{2} = 40

and

x = \frac{-64}{2} = -32

step 15

Since speed cannot be negative, the speed of the train is

x = 40

km/h

Answer

The speed of the train is 40 km/h

Key Concept

Solving quadratic equations

Explanation

We used the quadratic formula to solve for the speed of the train, ensuring that the solution is physically meaningful (i.e., non-negative).