Understanding the Bus Schedule Problem

This problem involves understanding a bus schedule based on regular intervals and calculating a specific time based on information given by an enquiry clerk. We are told that a bus leaves every 30 minutes and the next bus is scheduled for a specific time.

Determining the Previous Bus Departure Time

We know two key pieces of information about the bus schedule:

• The bus leaves every 30 minutes. This is the frequency or interval between buses.
• The next bus is scheduled to leave at $\text{9:35 AM}$.

Since buses leave at regular 30-minute intervals, the bus that departed just before the $\text{9:35 AM}$ bus must have left 30 minutes earlier.

We can calculate the departure time of the previous bus using subtraction:

Previous bus departure time = Next bus departure time - Frequency

Previous bus departure time = $\text{9:35 AM} - \text{30 minutes}$

To subtract 30 minutes from $\text{9:35 AM}$, we subtract 30 from the minute part:

$\text{35 minutes} - \text{30 minutes} = \text{5 minutes}$

So, the previous bus left at $\text{9:05 AM}$.

Calculating When the Information Was Given

The enquiry clerk, Ramesh, told Anil that the bus (referring to the one that just left) "had already left 10 minutes ago".

This means that the moment the clerk was speaking to Anil was exactly 10 minutes after the previous bus had departed.

We know the previous bus departed at $\text{9:05 AM}$.

The time the information was given = Previous bus departure time + Time elapsed since departure

The time the information was given = $\text{9:05 AM} + \text{10 minutes}$

To add 10 minutes to $\text{9:05 AM}$, we add 10 to the minute part:

$\text{05 minutes} + \text{10 minutes} = \text{15 minutes}$

So, the time the enquiry clerk gave the information to Anil was $\text{9:15 AM}$.

Step-by-Step Bus Time Calculation

1. Identify the departure time of the next bus: $\text{9:35 AM}$.
2. Identify the frequency of the bus service: Every $\text{30 minutes}$.
3. Calculate the departure time of the bus that left before the $\text{9:35 AM}$ bus: $\text{9:35 AM} - \text{30 minutes} = \text{9:05 AM}$.
4. Note the information given by the clerk: The previous bus left $\text{10 minutes ago}$.
5. Calculate the exact time the clerk gave the information by adding the elapsed time to the previous bus departure time: $\text{9:05 AM} + \text{10 minutes} = \text{9:15 AM}$.

Key Concepts in Solving Time and Schedule Problems

• Frequency: The regular interval at which an event occurs (e.g., bus leaves every 30 minutes).
• Elapsed Time: The amount of time that has passed since a specific event occurred.
• Relative Time Statements: Phrases like "X minutes ago" refer to a time point relative to the moment the statement is made.
• Working Backwards: Sometimes, starting from a known future time and using the frequency helps determine past event times.

Revision Table: Bus Schedule Details

Additional Information: Time Calculations

Time calculation problems often require careful reading of phrases like "ago," "in," "before," and "after." When dealing with time intervals and clocks, it's essential to remember that an hour has 60 minutes. Subtracting or adding time might require borrowing from or carrying over to the hour part.

For example, subtracting 30 minutes from $\text{10:10}$ AM:

• We need to subtract 30 from 10. Since 10 < 30, we borrow 1 hour (60 minutes) from the hour part.
• The hour becomes 9 ($\text{10} - \text{1}$).
• The minutes become $\text{10} + \text{60} = \text{70}$.
• Now subtract 30 minutes from 70 minutes: $\text{70} - \text{30} = \text{40}$ minutes.
• So, $\text{10:10 AM} - \text{30 minutes} = \text{9:40 AM}$.

In our specific problem, subtracting 30 minutes from $\text{9:35 AM}$ was straightforward because $\text{35} > \text{30}$. We simply subtracted 30 from 35 to get 5 minutes, keeping the hour as 9, resulting in $\text{9:05 AM}$. Adding 10 minutes to $\text{9:05 AM}$ was also simple as $\text{05} + \text{10} = \text{15}$, resulting in $\text{9:15 AM}$.