A train travels a distance of 300 km at a constant speed. If the speed of the train is
increased by 5 km/h, the journey would have taken 2 hours less. Find the original speed of the
train.
Given
- Distance travelled by the train = 300 km
- Let the original speed be x km/h.
- New speed = (x + 5) km/h
- The new journey time reduces by 2 hours.
Step 1: Form the Equation
We know:
Time = Distance ÷ Speed
- Original time = 300/x hours
- New time = 300/(x + 5) hours
According to the question:
300/x − 300/(x + 5) = 2
Step 2: Solve the Equation
300(x + 5) − 300x = 2x(x + 5)
1500 = 2x² + 10x
Bring all terms to one side:
2x² + 10x − 1500 = 0
Divide by 2:
x² + 5x − 750 = 0
Factorisation:
(x + 30)(x − 25) = 0
So,
x = −30 (not possible)
x = 25
Final Answer
The original speed of the train is 25 km/h.