Final answer:
The speed of the train is found by setting up two equations based on the original speed and time, and the new conditions when the speed is increased by 10 km/h. After substituting values and solving the resulting quadratic equation, we find that the original speed of the train is 30 km/h, which corresponds to option c.
Step-by-step explanation:
The student's question is to find the speed of the train given that it covers a distance of 360 km. If the speed had been 10 km/h faster, the train would have taken 3 hours less for the same journey. To solve this, let us denote the original speed of the train as V km/h. The time taken to cover the distance at this speed would be T hours, so V * T = 360. If the train's speed increases by 10 km/h, its new speed is V + 10 km/h, and the new time taken is T - 3 hours. The equation for the new speed and time would be (V + 10) * (T - 3) = 360.
We now have two equations derived from these relationships:
- V * T = 360
- (V + 10) * (T - 3) = 360
From the first equation, we get T = 360 / V. Substituting the value of T in the second equation gives us (V + 10) * (360/V - 3) = 360. By simplifying and solving the quadratic equation, we can determine the value of V. It turns out that V = 30 km/h is the speed of the train, which corresponds to option c.
Let's review the steps and the units. The original distance is given in kilometers, and speed is in km/h, so when we calculate time, we naturally get it in hours. The process uses standard algebraic manipulation and equation solving techniques. This calculation assumes constant speed, which means acceleration is ignored, as is typical for such problems.