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 in km/hr
Answers
The speed of the train is 25 km/hr.
let the normal speed of the train is s km/hr
Hence time taken by the train to cover 600 km = 600/s
Now the increased speed of the train is = s+5
so time taken by the train = 600/(s+5)
According to the given data:
Time taken with speed s -time taken with speed (s+5) = 4
=> 600/s - 600/(s+5) = 4
=> 1/s - 1/(s+5) = 1/150
=> (s+5 -s)/[s(s+5)] = 1/150
=> s² + 5s -750 = 0
Solving the eqn we get,
s = 25 or -30
neglecting -30 as speed cannot be negative , we get s = 25
Hence the speed of the train is 25 km/hr.
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)
Solve x:
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
(x - 25) (x + 30) = 0
x = 25 or x = - 30 (rejected, speed cannot be negative)
Find the speed of the train:
Speed = x = 25 km/h
Answer: The speed is 25 km/h