Question

A babysitter charges \(\$ 2.50\) an hour until 9: 00 PM when the rate drops to \(\$ 1.75\) an hour (the children are in bed). Write a program that accepts a starting time and ending time in hours and minutes and calculates the total babysitting bill. You may assume that the starting and ending times are in a single 24-hour period. Partial hours should be appropriately prorated.

Short answer

Calculate costs separately for pre and post 9 PM, then sum for the total bill.

Step-by-step solution

Understand the Problem

The babysitter's rates change throughout the evening. They charge $2.50 per hour until 9:00 PM and $1.75 per hour after 9:00 PM. You need to calculate the total charge based on a start and end time, where times are given in hours and minutes, and ensure partial hours are prorated.

Input Format

The input to the program should accept a starting time and an ending time, each specified in hours and minutes format, making sure both are within a single 24-hour period.

Calculate Different Time Spans

Determine the duration when the $2.50 rate applies (from the start time until 9 PM or the end time, whichever is earlier) and the duration when the $1.75 rate applies (from 9 PM until the end time, if applicable).

Prorate Hours if Necessary

Convert the hours and minutes into fractions of an hour to correctly calculate partial payments. For instance, 30 minutes should be represented as 0.5 hours.

Implement the Program Logic

Calculate the cost for the time worked before 9 PM at $2.50/hour and after 9 PM at $1.75/hour, each adjusted for partial hours if necessary.

Calculate Total Bill

Sum the charges from both time spans to determine the total babysitting bill.

Key concepts

Hourly Rate Calculation

Calculating the hourly rate is crucial in programming when dealing with specific charge rates based on time. In this exercise, the babysitter charges \(\\(2.50\) per hour until 9:00 PM and switches to \(\\)1.75\) per hour afterwards. To implement this in Python, you'll first define your rates:

• Rate 1 = \(\\(2.50\) (before 9:00 PM)
• Rate 2 = \(\\)1.75\) (after 9:00 PM)

Once you've assigned these rates, you can multiply them by the hours worked in each period to compute total earnings. Properly understanding how hourly rates apply to different time spans is essential for writing accurate programs dealing with time-based calculations.

24-hour Time Format

The 24-hour clock format is a straightforward way to represent time without the need for AM or PM. In programming, using this format reduces confusion and error in calculations.
The 24-hour format starts at midnight (00:00) and runs until midnight the next day (24:00), with hours ranging from 00 to 23. For this exercise, you'll enter start and end times in this format. For example:

• 8:00 PM is 20:00
• 9:00 PM is 21:00

The challenge lies in converting these times into a simple integer format or extracting hours and minutes separately, which is necessary to calculate the hourly rate accurately. Making this conversion properly ensures that programmers can apply conditions based on time, like rate changes post 21:00.

Prorating Partial Hours

Prorating partial hours is essential when time worked doesn't perfectly fit into whole hours.
This concept involves converting minutes into a fraction of an hour. For instance, 30 minutes would be equivalent to 0.5 hours. In Python, you can achieve this by dividing the number of minutes by 60:\[\text{Partial Hour} = \frac{\text{Minutes}}{60}\]This fractional representation is then used in the calculation of fees during each rate period. When you break down hours into fractions, it allows programs to more accurately calculate costs for periods that don't fill complete hours, enhancing the program's accuracy and fairness.

Program Logic Implementation

In implementing the program logic, start by acquiring and processing the input times. The logic must segment the work period into portions charged at each different rate, depending on whether the work occurred before or after 9:00 PM.
You need to calculate the total number of hours, prorate any partial hours, and apply the corresponding rates to each segmented time block.

• Use conditionals to separate time blocks before and after 21:00.
• Calculate partial hours as necessary using fractions of an hour.
• Apply appropriate hourly rates to these calculated hours.

Finally, sum the amounts calculated for each period to get the total bill. Implementing this logic requires understanding of Python functions, conditionals, and loops, allowing for a comprehensive solution to the given problem.