Questions: On a bicycle, Alicia rides for 5 hours and is 52 miles from her house. After riding for 8 hours, she is 82 miles away. What is Alicia's rate? miles per hour

Solution Steps

To find Alicia's rate, we need to determine the distance she traveled over a specific period and divide it by the time taken. We have two data points: after 5 hours, she is 52 miles away, and after 8 hours, she is 82 miles away. The difference in distance divided by the difference in time will give us her rate in miles per hour.

Alicia rides for 8 hours and is 82 miles away from her house. After 5 hours, she is 52 miles away. The distance traveled between these two points is given by: \[ \text{Distance} = \text{Distance at 8 hours} - \text{Distance at 5 hours} = 82 - 52 = 30 \text{ miles} \]

The time interval during which this distance was traveled is: \[ \text{Time} = \text{Time at 8 hours} - \text{Time at 5 hours} = 8 - 5 = 3 \text{ hours} \]

The rate \( r \) can be calculated using the formula: \[ r = \frac{\text{Distance}}{\text{Time}} = \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \text{ miles per hour} \]

Final Answer