Answer:
So let's just mke things easier by imagining that x (km/h) was the original speed of the train.
From the information, we can conclude that:
- The train's speed when it went from station A to the stopping point was x (km/h) => The time it took to finish the first half of its journey was 60/x (h)
- The speed of the train when it went from the stopping point to station B was
x + 12 (km/h) => The time it took to finish the other half of its journey was
60/x + 12 (h)
- The original time the train was supposed to take to finish the whole journey was 120/x (h)
Since the train still arrived at city B on schedule, we have:
120/x = 60/x + 60/x + 12 + 1/6
⇔ 6 × 120 × (x + 12) = 6 × 60 × (x+12) + 6 × 60x + x(x + 12)
⇔ 720x + 8640 = 360x + 4320 + 360x + x² + 12x
⇔ 720x - 360x - 360x - x² - 12x = -8640 + 4320
⇔ - x² - 12x = -4320
⇔ -x² - 12x + 4320 = 0
⇔ -x² + 60x - 72x + 4320 = 0
⇔ -x(x - 60) - 72(x - 60) = 0
⇔ (-x - 72)(x - 60) = 0
⇔ -x - 72 = 0 or x - 60 = 0
⇔ -x = 72 or x = 60
⇔ x = -72 or x = 60
Since we know that the time can't be a negative number, the only available option left is 60 km/h.