A person covers 2/15 of a journey by rail, 9/20 by tonga, and the remaining 10 km on foot. What is the total length of the journey?

Introduction / Context:Journeys expressed in fractional parts can be reconstructed by summing known fractions and tying the leftover fraction to a given absolute remainder.

Given Data / Assumptions:

• By rail = 2/15 of total D.
• By tonga = 9/20 of D.
• On foot = 10 km = remaining fraction of D.

Concept / Approach:Compute remaining fraction: 1 - (2/15 + 9/20). Set that fraction equal to 10/D and solve for D.

Step-by-Step Solution:

Verification / Alternative check:Check parts: Rail = 2/15 * 24 = 3.2 km; Tonga = 9/20 * 24 = 10.8 km; Remaining = 10 km; total = 24 km.

Why Other Options Are Wrong:They result from arithmetic errors in fraction addition or inversion.

Common Pitfalls:Failing to use common denominators when adding fractions; forgetting to equate the leftover fraction to 10/D.

Final Answer:24 km