Problem 40
Question
The distance from Melbourne to London is \(10,500 \mathrm{mi}\). If a jet averages 500 mph between the two cities, what is its travel time in hours?
Step-by-Step Solution
Verified Answer
21 hours.
1Step 1: Understand the Given Data
The problem states that the distance between Melbourne and London is 10,500 miles and the average speed of the jet is 500 miles per hour.
2Step 2: Use the Formula for Time
To find the time it takes to travel a certain distance at a certain speed, use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
3Step 3: Substitute the Given Values
Substitute the given values into the formula: \[ \text{time} = \frac{10,500 \text{ miles}}{500 \text{ mph}} \]
4Step 4: Simplify the Calculation
Divide 10,500 by 500 to find the travel time: \[ \text{time} = 21 \text{ hours} \]
5Step 5: State the Final Answer
The total travel time from Melbourne to London is 21 hours.
Key Concepts
distance calculationaverage speedtravel time
distance calculation
To solve distance-rate-time problems, the first step is understanding the concept of distance calculation.
Distance is simply how far an object travels.
In the exercise, we know the distance from Melbourne to London is 10,500 miles.
This is a key piece of information needed for our calculation.
You can think of distance like a large number line that measures how far something travels.
It’s crucial for solving any problem involving movement from one place to another.
In general, calculating distance involves knowing either the speed and time or having an initial distance value, like in our example.
Distance is simply how far an object travels.
In the exercise, we know the distance from Melbourne to London is 10,500 miles.
This is a key piece of information needed for our calculation.
You can think of distance like a large number line that measures how far something travels.
It’s crucial for solving any problem involving movement from one place to another.
In general, calculating distance involves knowing either the speed and time or having an initial distance value, like in our example.
average speed
Average speed is another essential concept when solving distance-rate-time problems.
In simple terms, average speed is the total distance traveled divided by the total time taken.
For this exercise, the jet has an average speed of 500 miles per hour.
Average speed helps in finding out how fast an object is moving over a particular period.
The formula for average speed can be written as:
\[ \text{speed} = \frac{\text{distance}}{\text{time}} \]
Knowing the average speed allows us to easily calculate other variables such as time or distance using simple algebra.
It is important because it gives a consistent rate to relate distance and time.
For example, if you know the speed of a jet, you can find out how long a trip will take for a given distance.
In simple terms, average speed is the total distance traveled divided by the total time taken.
For this exercise, the jet has an average speed of 500 miles per hour.
Average speed helps in finding out how fast an object is moving over a particular period.
The formula for average speed can be written as:
\[ \text{speed} = \frac{\text{distance}}{\text{time}} \]
Knowing the average speed allows us to easily calculate other variables such as time or distance using simple algebra.
It is important because it gives a consistent rate to relate distance and time.
For example, if you know the speed of a jet, you can find out how long a trip will take for a given distance.
travel time
Finally, travel time determines how long it takes for an object to move from one place to another.
For the given problem, we use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
By plugging in our known values: 10,500 miles (distance) and 500 miles per hour (speed), we get: \[ \text{time} = \frac{10,500 \text{ miles}}{500 \text{ mph}} = 21 \text{ hours} \]
Travel time tells us how long the journey will take.
This is important information for planning and scheduling.
Always remember that a longer distance or slower speed will increase travel time.
Conversely, a shorter distance or higher speed will decrease it.
Travel time can vary based on factors like speed limits, route changes, and other delays.
For the given problem, we use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
By plugging in our known values: 10,500 miles (distance) and 500 miles per hour (speed), we get: \[ \text{time} = \frac{10,500 \text{ miles}}{500 \text{ mph}} = 21 \text{ hours} \]
Travel time tells us how long the journey will take.
This is important information for planning and scheduling.
Always remember that a longer distance or slower speed will increase travel time.
Conversely, a shorter distance or higher speed will decrease it.
Travel time can vary based on factors like speed limits, route changes, and other delays.
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