To determine how much faster the runner's speed is compared to the swimmer's speed, we first need to calculate the runner's speed.
The runner completed a 200-meter dash in 21.3 seconds. The speed of the runner can be calculated using the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Substituting the values: \[ \text{Speed}_{\text{runner}} = \frac{200 \text{ meters}}{21.3 \text{ seconds}} \approx 9.396226415 \text{ meters per second} \]
Now, we can round this to the nearest tenth: \[ \text{Speed}_{\text{runner}} \approx 9.4 \text{ meters per second} \]
Next, we compare the runner's speed to the swimmer's speed. The swimmer's speed is given as 1.8 meters per second. To find how much faster the runner is than the swimmer, we subtract the swimmer's speed from the runner's speed: \[ \text{Difference in speed} = \text{Speed}{\text{runner}} - \text{Speed}{\text{swimmer}} = 9.4 \text{ m/s} - 1.8 \text{ m/s} = 7.6 \text{ m/s} \]
Thus, to the nearest tenth of a meter per second, the runner is 7.6 meters per second faster than the swimmer.
The answer is \( 7.6 \) meters per second.
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