Question

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.​

Answer 1

Step-by-step explanation:

Distance travelled by the train = 480 km Let the speed of the train be x kmph Time taken for the journey = 480/x Given speed is decreased by 8 kmph

Hence the new speed of train = (x – 8) kmph Time taken for the journey = 480/(x – 8)� 1280 = x2�– 8x �x2�– 8x – 1280 = 0 On solving we get x = 40

Thus the speed of train is 40 kmph

Answer 2

Given:

• Distance (d) = 480 km
• Speed (s) = 8km/h Less
• Time Taken (t) = 3 hours more

To Find:

• Speed of the Train

Solution:

Situation 1

Let speed of train = x km/h

And:

Time taken to travel 480 km = ( 480/x ) km/h

Situation 2

Speed of train = (x – 8) km/h

As given,

• The train will take 3 hours more to cover the same distance.

Therefore,

Time taken to travel 480 km = ( 480/x ) + 3 km/h

We Know that;

$\bigstar{\underline{\boxed{\tt\green{Speed_{(s)} \times Time_{(t)} = Distance_{(d)} }}}}$

After substituting values,

$\implies$ (x – 8) [( 480/x ) + 3] = 480

$\implies$ 480 + 3x – ( 3840/x ) – 24 = 480

$\implies$ 3x – (3840/x) = 24

$\implies$ 3x² – 24x – 3840 = 0

$\implies$ x² – 8x – 1280 = 0

Hence,

• x² – 8x – 1280 is the representation of the problem mathematically.

_______________________

$\implies$ x² – 8x – 1280

$\implies$ x² - (40 - 32)x - 1280

$\implies$ (x² - 40x) + (32x - 1280)

$\implies$ x(x - 40) + 32(x - 40)

$\implies$ (x - 40) (x + 32)

• (x - 40) $\implies$ x = 40
• (x + 32) $\implies$ x = -32

The Speed can't be Negative ( —ve ).

Hence,

• The Speed of the Train is 40 km/h.