A train covers 240 km at a uniform speed. If its speed is increased by 4 km/h, it takes 0.5 hour less. What is the original speed?
- 36 km/h
- 40 km/h
- 44 km/h
- 48 km/h
Explanation
Time at original speed = 240 / x
Time at increased speed = 240 / (x + 4)
Given:
240/x - 240/(x + 4) = 0.5
Multiply through by x(x + 4) to eliminate denominators:
240(x + 4) - 240x = 0.5x(x + 4)
240x + 960 - 240x = 0.5x² + 2x
960 = 0.5x² + 2x
Multiply both sides by 2:
1920 = x² + 4x
x² + 4x - 1920 = 0
Solve the quadratic:
x² + 4x - 1920 = 0
Using quadratic formula:
x = [-4 ± √(16 + 7680)] / 2
x = [-4 ± √7696] / 2
√7696 ≈ 87.7
x ≈ (-4 + 87.7)/2 ≈ 83.7/2 ≈ 41.85
Approximate correct option is 40 km/h
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