Final answer:
Paul travelled by train for a distance of x, which is 45 km. This was three-fourths of his entire trip. The rest of his trip was taken by bus and then by walking, where the walking distance was 9 km.
Step-by-step explanation:
To solve for the value of x, which represents the distance Paul travelled by train and forms three-fourths of his whole trip, we use the information that the remaining part of the trip is divided into two parts: a bus ride and walking. First, let's denote the entire journey as T. Since three-fourths of the journey is by train, we have x = ¾T. The remaining ¼T is split into two parts: two-fifths by bus and the rest, 9km, by walking.
The fraction of the journey by bus is ¾T × ¾ = ⅗T. So, the walking distance is given by W = ¼T - ⅗T. We know that W = 9 km, so we can set up the equation ¼T - ⅗T = 9 km to solve for T. Re-arranging and solving for T gives T = 60 km. Now we have the total distance of the trip, and we can find x by calculating ¾ of 60 km, which gives us x = 45 km.
Finally, for sanity check and to ensure the answer is reasonable, we can calculate the remaining distances again with T = 60 km and verify that they match the given information.