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?
Formula For Speed
let the uniform speed of Train
and the time taken to complete distance
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
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
Suppose the speed of the train is
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
#480x = 480(x-8) +3x(x-8)#
- Deform and factorize the equation to solve it.
Don't forget that the answer must be positive, so the speed
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.