Questions: A runner completed a marathon in 3 hours and 34 minutes. What was her average speed, in meters per second? 1 marathon = 26.2 miles. 1 mile = 1.609 kilometers. 3.91 meters / second 1.27 meters / second 3.28 meters / second 7.34 meters / second

Solution Steps

First, we need to convert the marathon distance from miles to meters.

Given:

• 1 marathon = 26.2 miles
• 1 mile = 1.609 kilometers
• 1 kilometer = 1000 meters

So, the distance in meters is: \[ 26.2 \text{ miles} \times 1.609 \text{ km/mile} \times 1000 \text{ m/km} = 42195.8 \text{ meters} \]

Next, we convert the time from hours and minutes to seconds.

Given:

• 3 hours and 34 minutes

Convert hours to minutes: \[ 3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes} \]

Add the additional minutes: \[ 180 \text{ minutes} + 34 \text{ minutes} = 214 \text{ minutes} \]

Convert minutes to seconds: \[ 214 \text{ minutes} \times 60 \text{ seconds/minute} = 12840 \text{ seconds} \]

Now, we calculate the average speed using the formula: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Substitute the values: \[ \text{Average speed} = \frac{42195.8 \text{ meters}}{12840 \text{ seconds}} \approx 3.2850 \text{ meters/second} \]

Final Answer