Final answer:
To solve for the train's speed, we set up an equation based on the information given and solved the resulting quadratic equation. The original speed of the train is found to be 45 km/h.
Step-by-step explanation:
To find the speed of the train, let's denote the original speed as v km/h. The time taken to travel 360 km at this speed is 360/v hours. If the train's speed increased by 5 km/h, the new speed would be (v + 5) km/h, and the time taken would now be 360/(v + 5) hours, which is 1 hour less than the original time. Hence, we can set up the equation:
360/v - 1 = 360/(v + 5)
Multiplying both sides by v(v + 5) to get rid of the denominators, we get:
360(v + 5) - v(v + 5) = 360v
Expanding and simplifying the equation, we get:
360v + 1800 - v² - 5v = 360v
Combining like terms and moving them to one side:
v² + 5v - 1800 = 0
Factoring the quadratic equation gives us:
(v - 45)(v + 40) = 0
Since speed cannot be negative, we discard the negative root, leaving v = 45 km/h as the solution.
Thus, the speed of the train is 45 km/h, which corresponds to option (a).