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:

Let the speed be X

= Time = Distance/Speed = 480/x

According to the Q, If the speed would have been 8km/h less (x-8) then the time would have been 3 hours more (480/x + 3)

Speed = Distance / Time

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

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

Answer 2

Solution:

Let Suppose;

Speed of train = x km/h

And

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

As per second situation, the 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

As we know,

Speed × Time = Distance

Therefore,

(x – 8)[(480/x) + 3] = 480

⇒ 480 + 3x – (3840/x) – 24 = 480

⇒ 3x – (3840/x) = 24

⇒ 3x² – 24x – 3840 = 0

⇒ x² – 8x – 1280 = 0

Hence,

x² – 8x – 1280 = 0 is the required representation of the problem mathematically.