Distance Problems | Time and Distance Aptitude Practice | Kuriloo

Fundamental Principles

Distance

The linear path length covered by a moving entity, calculated using the standard equation: $Distance = Speed \times Time$.

Essential Formulation Tips

When a problem describes early or late arrivals, use the difference between those time values to set up an algebraic timeline balance.
Ensure any time differences stated in minutes are divided by 60 to convert them to hours before pairing them with speeds in km/h.

Shortcut Execution Techniques

The Early-Late Product Shortcut: If an object covers a route at speed $S_1$ and arrives $t_1$ late, and covers it at speed $S_2$ arriving $t_2$ early, the total distance is: $D = \frac{S_1 \times S_2}{|S_1 - S_2|} \times (\text{Total Time Difference})$.

Contextual Inquiries (FAQs)

Q: How do I calculate the 'Total Time Difference' if a traveler is 10 minutes late in scenario A and 5 minutes early in scenario B?

A: Because the scenarios fall on opposite sides of the scheduled arrival time, add the intervals together: $10 \text{ minutes} + 5 \text{ minutes} = 15 \text{ minutes} = \frac{15}{60} \text{ hours} = 0.25 \text{ hours}$.

Example Breakdown: Solving Early/Late Commute Deviations

Classic product-over-difference shortcut problem.

Problem QueryA student walking at 4 km/h reaches school 5 minutes late. If they walk at 5 km/h instead, they arrive 10 minutes ahead of schedule. Find the total distance from their home to school.

Step-By-Step Solution Path

Identify given speed values: $S_1 = 4 \text{ km/h}$, $S_2 = 5 \text{ km/h}$.

Calculate total time variance: One scenario is 5 mins late, the other is 10 mins early. Total offset = $5 + 10 = 15 \text{ minutes}$.

Convert time offset to hours: $\text{Time Difference} = \frac{15}{60} = \frac{1}{4} \text{ hour}$.

Apply the product-difference shortcut equation: $D = \frac{S_1 \times S_2}{|S_1 - S_2|} \times \Delta T$.

Substitute values into your equation: $D = \frac{4 \times 5}{|4 - 5|} \times \frac{1}{4} = \frac{20}{1} \times \frac{1}{4}$.

Perform final fraction reduction: $D = 5 \text{ km}$.

Conclusion: The total distance to school is 5 km.

Analytical Hint: Multiply your two speeds together, divide by their difference, and multiply that by your total time offset in hours.

Route Isolation Challenges

Practice working backward from time changes to calculate unknown route distances.

Q1. A delivery driver traveling at 60 km/h is 1 hour late. If they speed up to 80 km/h, they arrive exactly on time. What is the total delivery distance?