Example 3- Distance-time graphs
The distance graph shows the height of a plane as it completes a journey.
When the plane is at a height of 38,000 feet (ft), it travels at a constant speed of 550 miles per hour.
How far does it travel while it is flying at 38,000 ft?
Solution
1. What do I have to do?
Read the question through twice.
Highlight or underline the important pieces of information in the question.
2. What information do I need?
The highlighted words are the most important ones.
What is the question asking?
The question asks how far the plane travels at 38,000 ft.
The 38,000 ft is relevant as the plane is not always travelling at this height.
The speed is given in miles per hour, therefore the answer should be in miles.
To work out distance, the following formula can be rearranged:
\(\text{speed} = \frac{\text{distance}}{\text{time}}\)
3. What information don’t I need?
Sometimes information given is not needed or important.
However everything in this question is relevant to working out the answer.
4. What maths can I do?
Step A
Check how long the plane is travelling at 38,000 ft by highlighting the line on the graph.
One large square is worth 1 hour or 60 minutes. Five small squares make up one large square so divide 60 minutes by 5 to work out what each small square is worth.
\(60 \div 5 = 12~\text{minutes}\)
Therefore each small square is worth 12 minutes.
The plane is at 38,000 ft for 3 full large squares and 8 small squares which equates to 3 hours and 96 minutes, or more simply 4 hours and 36 minutes.
Step B
\(\text{Distance} = \text{speed} \times \text{time}\)
Before using this formula, 4 hours 36 minutes needs to be converted to just hours.
Do this by dividing the minutes by 60 (because there are 60 minutes in an hour).
\(36 \div 60 = 0.6\)
Therefore the time taken is 4.6 hours.
Step C
Now use the formula to work out the distance the plane travelled.
\(\text{Distance} = \text{speed} \times \text{time}\)
Distance = \(550 \times 4.6\)
Distance = 2,530 miles.
Therefore the plane travelled 2,530 miles at 38,000 ft.
5. Is my solution correct?
It is important to check any calculations at the end.
6. Have I completed everything?
The answer is a distance and is in miles, which is how it should be.
Make sure the answer has the units on it.
Nothing else was asked for.