# 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. What is the speed of the train?

##### 2 Answers

#### Explanation:

Total Distance

Formula For Speed

Hence

Case-I

let the uniform speed of Train

and the time taken to complete distance

Distance **(equation 1)**

Case-II

If speed has been 8km/h less then train would have taken 3 hours more to cover the same distance.

Now in this situation

speed of train

and Time taken to complete distance

Distance **(equation 2)**

Since Distance for both cases are same .

Comparing **equation 1** and **equation 2**, we get

cancel **vt** from both side

but from **equation 1** the value of

factorize the quadratic equation

Speed is Positive hence

#### Explanation:

Suppose the speed of the train is

It takes

8 km/h slower, it would take

Now we've got the equation:

This can be solved as follows.

- Multiple both sides of the equation by
#x(x-8)# .

#480x = 480(x-8) +3x(x-8)# - Deform and factorize the equation to solve it.

#x^2-8x-1280=0#

#(x-40)(x+32)=0#

#x=40, -32#

Don't forget that the answer must be positive, so the speed

is

Let's check.

If we travel at 40 km/h, it takes 12 hours.

If we traveled at 32 km/h, it would take 15 hours, so the difference

is three hours and we've got the correct answer.