Vishnu travels three equal distances at speeds of 10 km/h, 30 km/h, and 8 km/h, taking a total of 15.5 minutes to complete the journey. What is the total distance he travels in kilometres?

Introduction / Context:
This question is about motion in three stages where equal distances are travelled at different speeds. It tests your ability to set up an equation based on total time and to convert between minutes and hours correctly. Such problems are typical in competitive exams and require both algebraic thinking and unit management.

Given Data / Assumptions:
Vishnu travels an equal distance d in each of three segments.
Speed in the first segment = 10 km/h.
Speed in the second segment = 30 km/h.
Speed in the third segment = 8 km/h.
Total time for all three segments combined = 15.5 minutes.
We must find the total distance travelled, that is 3d, in kilometres.

Concept / Approach:
Time taken for each segment is distance divided by speed. Since the distances are equal, we can express total time as the sum of three such fractions. The total time is given in minutes, so we first convert it to hours. Then we solve the equation for d. Finally, total distance becomes 3d. This approach is a direct application of the time formula and algebraic solving of a linear equation.

Step-by-Step Solution:
Step 1: Let each segment distance be d km.Step 2: Convert total time from minutes to hours. 15.5 minutes = 15.5 / 60 hours.Step 3: 15.5 minutes is 31 / 2 minutes, so in hours it is (31 / 2) / 60 = 31 / 120 hours.Step 4: Time for first segment = d / 10 hours.Step 5: Time for second segment = d / 30 hours.Step 6: Time for third segment = d / 8 hours.Step 7: Total time equation: d / 10 + d / 30 + d / 8 = 31 / 120.Step 8: Factor out d: d * (1 / 10 + 1 / 30 + 1 / 8) = 31 / 120.Step 9: Compute 1 / 10 + 1 / 30 + 1 / 8. The common pattern gives this sum as 31 / 120.Step 10: So d * (31 / 120) = 31 / 120.Step 11: Divide both sides by 31 / 120 to get d = 1 km.Step 12: Total distance travelled = 3d = 3 * 1 = 3 km.

Verification / Alternative check:
If each segment is 1 km, then times are: first segment 1 / 10 h = 6 minutes; second segment 1 / 30 h = 2 minutes; third segment 1 / 8 h = 7.5 minutes. Total time = 6 + 2 + 7.5 = 15.5 minutes, which matches the problem statement. This confirms that the distances and times are consistent, and the total distance is indeed 3 km.

Why Other Options Are Wrong:
1 km would correspond to the distance of only one segment, not the entire journey.
2 km or 4 km do not satisfy the total time equation when you recompute the segment times using the given speeds.
5 km is too large and leads to times that exceed 15.5 minutes when recalculated correctly.

Common Pitfalls:
Students often forget to convert minutes into hours, leading to wrong equations. Some also mistakenly assume the same time is spent at each speed instead of the same distance. Another error is to treat 15.5 minutes incorrectly as 15 minutes and 50 seconds. Always convert time into a fraction of an hour carefully and then form the correct equation.

Final Answer:
Vishnu travels a total distance of 3 km.