Formula for a train travels a distance of 600 km at a constant speed. if the speed of the train is increased by 5 km/hr, the journey would take 4 hrs less. find the speed of the train.
Answers
Let the speed of the train be x.
When the speed is increased by 5 it becomes :
x + 5
The time taken before the speed is increased is 600/x
The time taken after the speed is increased is :
600/(x + 5)
This is 4 hrs less than the time it was to take before the speed is increased.
We equate this as below :
600/x = 600/(x + 5) + 4
600(x + 5) = 600x + 4x (x + 5)
600x + 3000 = 600x + 4x² + 20x
4x² + 20x - 3000 = 0
Dividing through by 4:
x² + 5x - 750 = 0
The roots of this quadratic equation are :
+30, - 25
x² + 30x + 25x - 750 = 0
x(x + 30) - 25(x + 30) = 0
(x - 25) (x + 30) = 0
x = 25 or - 30
We pick the positive value since velocity is positive.
The speed of the train is thus :
25 km/h
Let the speed be x km/h
When the train was traveling at original speed:
Distance = 600 km
Speed = x km/h
Time = Distance ÷ Speed
Time = 600/x
When train was increased by 5 km/h:
Distance = 600 km
Speed = (x + 5) km/h
Time = Distance ÷ Speed
Time = 600/(x + 5)
Given that the time needed is 4 hour lesser
600/x - 600/(x + 5) = 4
600(x + 5) - 600 = 4x(x + 5)
600x + 30000 - 600x= 4x² + 20x
4x² + 20x - 3000 = 0
x² + 5x - 750 = 0