Final answer:
Jane travels 2/3 of her journey by train, 7/8 of the remaining 1/3 by bus, and the remainder by motorcycle. The bus part is 3 km more than the motorcycle part. By setting up an equation and solving it, we find that her total journey is 12 kilometers long.
Step-by-step explanation:
To solve the problem of Jane's journey, we must consider the portions of travel by different modes of transportation and their relationship. Jane travels 2/3 of her journey by train. The remainder of the journey would then be 1 - 2/3, which is 1/3. Now, she travels 7/8 of this 1/3 by bus. If we call the total journey 'x' km, this part would be (7/8)*(1/3)*x km. The rest of the journey, which is 1/8 of the 1/3 remaining journey, is by motorcycle, which amounts to (1/8)*(1/3)*x km.
We are given that the bus distance is 3 km longer than the motorcycle distance. Therefore:
(7/8)*(1/3)*x = (1/8)*(1/3)*x + 3
By solving this equation, we can find the total length of Jane's journey. Simplifying the equation:
(7/24)*x = (1/24)*x + 3
To isolate 'x,' we subtract (1/24)*x from both sides:
(6/24)*x = 3
(1/4)*x = 3
Now, multiply both sides by 4 to solve for 'x':
x = 12 km
Thus, Jane's total journey is 12 kilometers long.