Time Problems | Time and Distance Aptitude Practice | Kuriloo

Fundamental Principles

Time

The total chronological duration of travel, calculated using the equation: $Time = \frac{Distance}{Speed}$.

Essential Formulation Tips

When tracking transit delays, remember that station stops reduce a vehicle's effective overall speed without changing its actual top running speed.
Keep travel time values separated from stationary rest intervals when setting up your equations.

Shortcut Execution Techniques

The Rest Time Exclusion Rule: The stoppage time per hour for a transit vehicle is calculated using the formula: $\text{Stoppage Time Per Hour} = \frac{\text{Speed}_{\text{excluding stops}} - \text{Speed}_{\text{including stops}}}{\text{Speed}_{\text{excluding stops}}}$.

Contextual Inquiries (FAQs)

Q: How do constant station stops change a transit vehicle's average speed?

A: Stops increase the total time value in the denominator of your calculation while distance stays constant, which lowers the overall average speed for the trip.

Example Breakdown: Calculating Transit Rest-Stop Delays

Standard hourly rest-stop reduction calculation.

Problem QueryA passenger bus travels at an average rate of 54 km/h when running without stops, but averages only 45 km/h when factoring in station stops. How many minutes per hour does the bus spend stopped?

Step-By-Step Solution Path

Identify baseline running speeds: $\text{Speed}_{\text{flat}} = 54 \text{ km/h}$, $\text{Speed}_{\text{stops}} = 45 \text{ km/h}$.

Calculate the speed reduction caused by stopping: $54 - 45 = 9 \text{ km/h}$.

Apply the rest time rule formula: $\text{Stoppage Proportion} = \frac{\text{Reduction}}{\text{Speed}_{\text{flat}}} = \frac{9}{54}$.

Reduce the fraction to find the hourly proportion: $\frac{9}{54} = \frac{1}{6}$ of an hour.

Convert the fractional hour value into minutes: $\frac{1}{6} \times 60 \text{ minutes} = 10 \text{ minutes}$.

Conclusion: The bus spends an average of 10 minutes per hour stopped at stations.

Analytical Hint: Find the drop in speed, divide it by the faster non-stop speed, and multiply by 60 to get your minutes per hour.

Duration Allocation Control

Practice finding travel times and calculating rest delays across fixed routes.

Q1. Excluding station stops, a train runs at 80 km/h; including stops, it runs at 60 km/h. How many minutes per hour does the train stop?