Rubi walks from her home to a multiplex. At a speed of 3 km/h she reaches 5 minutes late, while at a speed of 4 km/h she reaches 5 minutes early. What is the distance in kilometres between her home and the multiplex?

Introduction / Context:

This question is very similar to the earlier example with Ram and his school. It involves early and late arrival times for two different walking speeds. Such problems test your ability to convert minutes into hours, form equations using time = distance / speed, and use the difference in times to deduce the unknown distance. These patterns repeat often in competitive examinations.

Given Data / Assumptions:

• Speed in the first case = 3 km/h and Rubi is 5 minutes late.
• Speed in the second case = 4 km/h and Rubi is 5 minutes early.
• Let the scheduled travel time be T hours.
• Let the distance between home and the multiplex be D kilometres.
• The path is the same and speeds are constant in each case.

Concept / Approach:

Again, we use time = distance / speed. At the lower speed, the time taken equals the scheduled time plus the amount of lateness. At the higher speed, the time taken equals the scheduled time minus the amount by which she is early. The difference between these two times equals the total difference between late and early arrivals. Solving the resulting equation allows us to find D directly.

Step-by-Step Solution:

Verification / Alternative check:

We can verify by computing the actual times. If D = 2 km, at 3 km/h time = 2 / 3 hour = 40 minutes. At 4 km/h time = 2 / 4 hour = 30 minutes. The difference between these times is 10 minutes. That exactly matches the total variation, since Rubi is 5 minutes late in one case and 5 minutes early in the other, giving a total difference of 10 minutes. Thus the value D = 2 km fits the entire situation correctly.

Why Other Options Are Wrong:

If the distance were 5 km, the times at 3 and 4 km/h would differ by far more than 10 minutes. Distances of 2.5 km or 5.5 km would similarly produce mismatched time differences. Only 2 km gives precisely a 10 minute difference between the two travel times and matches the early and late conditions described in the question.

Common Pitfalls:

Learners sometimes treat the difference between late and early as 0 minutes instead of adding the two 5 minute intervals. Another mistake is to convert minutes incorrectly or to forget that 5 minutes equals 5/60 hours. It is also easy to attempt guessing the distance rather than setting up an equation, which becomes unreliable as the numbers change. Systematic use of time = distance / speed is the safest method.

Final Answer:

The distance between Rubi’s home and the multiplex is 2 kilometres.