How can you determine who is running faster, Anne or John?
Understand the Problem
The question is asking to compare the speeds of Anne and John based on the information provided. It presents Anne's speed as 6 miles per hour and a table that shows John's distance at various time intervals. To determine who is running faster, we need to calculate John's speed from the table and compare it with Anne's speed.
Answer
John runs faster than Anne at 7 mph compared to Anne’s 6 mph.
Answer for screen readers
John is running faster than Anne during the time intervals from 0.5 to 1.5 hours.
Steps to Solve
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Identify Anne's Speed Anne's speed is given as 6 miles per hour.
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Extract John’s Mile Markers From the table, we gather the mile markers corresponding to John's times:
- At 0 hours: Mile Marker 4.0
- At 0.5 hours: Mile Marker 4.5
- At 1.0 hours: Mile Marker 8.0
- At 1.5 hours: Mile Marker 11.5
- Calculate Distances for John Next, we calculate the distance John runs at each time interval:
- From 0 to 0.5 hours:
- Distance = $4.5 - 4 = 0.5$ miles
- From 0.5 to 1 hour:
- Distance = $8 - 4.5 = 3.5$ miles
- From 1 to 1.5 hours:
- Distance = $11.5 - 8 = 3.5$ miles
- Calculate John's Speed To find John's speed, use the formula for speed:
$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$
Calculating for each time interval:
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For first interval (0 to 0.5 hours):
- Speed = $\frac{0.5 \text{ miles}}{0.5 \text{ hours}} = 1 \text{ mph}$
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For second interval (0.5 to 1 hour):
- Speed = $\frac{3.5 \text{ miles}}{0.5 \text{ hours}} = 7 \text{ mph}$
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For third interval (1 to 1.5 hours):
- Speed = $\frac{3.5 \text{ miles}}{0.5 \text{ hours}} = 7 \text{ mph}$
- Compare Speeds Now, we can compare John's calculated speeds to Anne's speed.
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John's speed varies:
- First interval: $1 \text{ mph}$
- Second and third intervals: $7 \text{ mph}$
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Anne's constant speed: $6 \text{ mph}$
John runs faster than Anne in the second and third intervals.
John is running faster than Anne during the time intervals from 0.5 to 1.5 hours.
More Information
While Anne maintains a steady speed of 6 mph, John's speed increases significantly during his runs, especially in the last two intervals where he reaches 7 mph.
Tips
- Miscalculating distances based on mile markers can lead to incorrect speed calculations. Always ensure you subtract the starting position from the ending position accurately.
- Forgetting to convert time differences properly when calculating speed.
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