Question

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

Given:  a train travels a distance of 480km at a uniform speed if the speed had been 8 km less, then it would have taken 3 hours more to cover the same distance  

To Find :  speed of the train

Solution:

Let  Say uniform speed of Train = S km/hr

Distance Covered  = 480 km

Using Formula  

Time = Distance/Speed

=> Time Taken  = 480/S  hr

Speed if 8 km less => S - 8 km/hr

time take = 480/(S - 8) hr

time taken is 3 hr more

=> 480/(S - 8)  = 480/S  + 3

multiplying both sides by S(S - 8)

=> 480S  = 480(S - 8)  + 3S(S - 8)

=> 480S = 480S  - 3840 + 3 S² - 24S

=>  3S² - 24S  - 3840 = 0

=> S² - 8S - 1280 = 0

=>  S²  + 32S - 40S - 1280 = 0

=> S(S + 32) - 40(S + 32) = 0

=> (S - 40)(S + 32) = 0

=> S = 40      S = -32 ( not possible)

Speed of the train = 40 km/hr

Speed of the train = 40 km/hr

Learn More:

1) A journey of 240 km would take half an hour less if the speed ...

https://brainly.in/question/10003391

Train takes 3 hours less for a journey 400 km, if its speed is incresed ...

https://brainly.in/question/7377990

A train travels 260 km at a uniform speed. If the speed had been 5 ...

https://brainly.in/question/17096139

Answer 2

Answer:

40 Km / h

Step-by-step explanation:

Distance traveled by train = 480 Km

Let the speed of the train be ' x ' Km / h

We know that

Speed = Distance / Time

⇒ Time = Distance / Speed

Time taken to travel 480 Km with the uniform speed ' x ' Km/h ( T ) = 480 / x hours

Given :

If the speed is reduced to 8 Km/h uniformly it would take 3 hours more to cover the same distance.

Speed of the train if it is reduced by 8 Km / h = ( x - 8 ) Km / h

⇒ Time = Distance / Speed

Time taken to travel 480 Km/h with the uniform speed ( x - 8 ) Km / h ( T' ) = 480 / ( x - 8 ) hours

According to the question :

⇒ T' = T + 3

⇒ T' - T = 3

⇒ 480/( x - 8 ) - 480/x = 3

$\Rightarrow \sf \dfrac{480x - \{480(x - 8) \}}{x(x - 8)} = 3$

$\Rightarrow \sf \dfrac{480x - 480x + 3840}{x^{2} - 8x} = 3$

⇒ 3840 / ( x² - 8x ) = 3

Dividing by 3 on both sides

⇒ 3840 / 3( x² - 8x ) = 3 / 3

⇒ 1280 / ( x² - 8x ) = 1

⇒ 1280 = x² - 8x

⇒ x² - 8x - 1280 = 0

⇒ x² - 40x + 32x - 1280 = 0

⇒ x( x - 40 ) + 32( x - 40 ) = 0

⇒ ( x + 32 )( x - 40 ) = 0

⇒ x + 32 = 0 OR x - 40 = 0

⇒ x = - 32 ( neglected as speed can't be negative ) OR x = 40

⇒ x = 40

Hence the speed of the train is 40 Km / h.