Solving the quadratic equation \( n^2 + n - 420 = 0 \):
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- Setting \( S = 210 \):
- \( \frac{n(n + 1)}{2} = 210 \)
- \( n(n + 1) = 420 \)
- \( n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm \sqrt{1681}}{2} = \frac{-1 \pm 41}{2} \)
- Taking the positive solution: \( n = \frac{40}{2} = 20 \).
- A train travels 300 km at a speed of 60 km/h and then another 200 km at a speed of 80 km/h. What is the train's average speed for the entire journey?
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