A train travels between P and Q in 3 hours.When the speed of train is increased by 6 km/hr,then it covers the same distance in 2 hours. What is original speed of train? Also find the distance between P and Q?
Question
A train travels between P and Q in 3 hours.When the speed of train is increased by 6 km/hr,then it covers the same distance in 2 hours. What is original speed of train? Also find the distance between P and Q?
Solution
Let's denote the original speed of the train as V (km/hr) and the distance between P and Q as D (km).
Step 1: From the problem, we know that the train covers the distance D in 3 hours at the original speed. So we can write the first equation as: D = V * 3.
Step 2: When the speed of the train is increased by 6 km/hr, it covers the same distance in 2 hours. So we can write the second equation as: D = (V + 6) * 2.
Step 3: Now we have a system of two equations, and we can solve it. Since both equations are equal to D, we can set them equal to each other: V * 3 = (V + 6) * 2.
Step 4: Simplify the equation: 3V = 2V + 12.
Step 5: Solve for V: V = 12 km/hr. So the original speed of the train is 12 km/hr.
Step 6: Substitute V = 12 into the first equation to find D: D = 12 * 3 = 36 km. So the distance between P and Q is 36 km.
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