Answer:
To find Eureka's rate, we need to determine the distance she travels in each hour.
We are given that after riding for 6 hours, Eureka is 24 miles away from her house. This means she is traveling at a rate of 24 miles divided by 6 hours, which is 4 miles per hour.
Next, we are told that after riding for 11 hours, Eureka is 39 miles away from her house. To find the distance she traveled in the last 5 hours, we subtract the initial distance of 24 miles from the final distance of 39 miles. This gives us 39 - 24 = 15 miles.
Therefore, in the last 5 hours, Eureka traveled 15 miles. To find her rate during this time, we divide the distance of 15 miles by the time of 5 hours, which gives us a rate of 15/5 = 3 miles per hour.
So, Eureka's rate in the first 6 hours was 4 miles per hour, and her rate in the next 5 hours was 3 miles per hour.
As for the second part of the question, "How far away from her house did she start riding?", we can add the distance she traveled in the first 6 hours (24 miles) to the distance she traveled in the next 5 hours (15 miles). This gives us a total distance of 24 + 15 = 39 miles.
Therefore, Eureka started riding 39 miles away from her house.