To solve this problem, let's break it down step by step.
1. Identify the given information:
- Juan can cross the bridge in 6 minutes.
- We need to determine the length of the bridge in meters.
- The average speed provided in the answer choices is 8 kilometers per hour (km/h).
2. Convert the speed from kilometers per hour to meters per minute:
- Since 1 kilometer is equivalent to 1000 meters, we first convert the speed into meters per hour.
- [tex]\( 8 \, \text{km/h} \times 1000 \, \text{meters/km} = 8000 \, \text{meters per hour} \)[/tex]
- Next, convert the speed into meters per minute by dividing the speed in meters per hour by the number of minutes in an hour (60 minutes).
- [tex]\( \frac{8000 \, \text{meters per hour}}{60 \, \text{minutes}} = 133.33 \, \text{meters per minute} \)[/tex] (rounded to two decimal places)
3. Calculate the length of the bridge:
- We know Juan crosses the bridge in 6 minutes.
- If Juan travels at 133.33 meters per minute, the length of the bridge can be found by multiplying his speed by the time it takes to cross the bridge.
- [tex]\( 133.33 \, \text{meters per minute} \times 6 \, \text{minutes} = 800.0 \, \text{meters} \)[/tex]
Therefore, the length of the bridge is 800 meters.
The correct answer is:
E. 800
