Problem 72 - Elementary Algebra

Question

In November 2007 , U.S. airlines had 415,024 scheduled departures. Find the number of flights that landed close to their scheduled arrival time. Round to the nearest whole number. (Source: www.bts.gov) U.S. airlines brought four-fifths of their November flights in close to schedule, making the month the second best of last year for on-time performance. (Source: www.usatodaycom, Jan. 8, 2008)

Step-by-Step Solution

Answer

332,019 flights landed close to their scheduled arrival time.

Step 1: Identify the Given Information

The total number of scheduled departures in November 2007 was 415,024. It is also given that U.S. airlines brought four-fifths of their flights in close to schedule.

Step 2: Determine the Fraction Representing On-Time Flights

Four-fifths of the flights were close to their scheduled arrival time. This can be represented by the fraction \(\frac{4}{5}\).

Step 3: Calculate the Number of On-Time Flights

Multiply the total number of scheduled departures by the fraction of on-time flights: \(\frac{4}{5} \times 415,024\).

Step 4: Perform the Multiplication

Calculate \(\frac{4}{5} \times 415,024\): \(\frac{4 \times 415,024}{5} = \frac{1,660,096}{5} = 332,019.2\).

Step 5: Round to the Nearest Whole Number

Since the number 332,019.2 of on-time flights is to be rounded to the nearest whole number, the final number of on-time flights is 332,019.

Key Concepts

scheduled departures

Scheduled departures refer to the total number of flights that are planned to depart from the airport according to the airline schedule. In November 2007, U.S. airlines had a total of 415,024 scheduled departures. This includes all flights that were planned to take off during the month.

Knowing the number of scheduled departures is important. It helps us understand the scale of operations and allows us to calculate performance metrics, such as on-time arrival rates. Airlines strive to adhere to this schedule to provide reliable service to passengers.

fraction of on-time flights

A fraction is a mathematical way to represent parts of a whole. In this problem, four-fifths of the flights landed close to their scheduled arrival time, which can be written as the fraction \(\frac{4}{5}\).

To calculate the number of on-time flights:

• Write down the total number of scheduled departures: 415,024.
• Multiply this number by the fraction of on-time flights: \(\frac{4}{5} \times 415,024\).
• The multiplication result is \(\frac{4 \times 415,024}{5} = \frac{1,660,096}{5} = 332,019.2\).

This means that out of 415,024 scheduled flights, 332,019.2 flights were on time.

rounding to nearest whole number

When calculating percentages or fractions, sometimes we end up with decimals. In many cases, including this one, it may be necessary to round to the nearest whole number. Rounding helps in simplifying the data for better understanding and communication.

The rounded number of on-time flights here is 332,019.2, which we need to round to the nearest whole number:

• Identify the digit at the first decimal place (in this case, 2 from 332,019.2).
• If this digit is 5 or higher, we round up. If it is 4 or lower, we round down.
• Since 2 is less than 4, we round down to 332,019.

So, 332,019 flights landed close to their scheduled arrival time.