Final answer:
Harvey the wonder hamster runs 3 1/6 km in 1/4 hour. By converting the mixed number into an improper fraction and multiplying by 4, we calculate that Harvey can run 12 2/3 km in one hour, which corresponds to option 4 from the question.
Step-by-step explanation:
To find out how far Harvey the wonder hamster can run in one hour, we need to calculate his running speed based on the distance covered in a given time frame and then extend that to cover a full hour.
First, let's establish Harvey's running pace. We know that Harvey can run 3 1/6 km in 1/4 hour. To express the distance in kilometres fully, convert the mixed number to an improper fraction equivalent: 3 1/6 km is the same as (3 \* 6 + 1)/6 km, or 19/6 km.
If Harvey runs 19/6 km in 1/4 hour, we can find out how many kilometres he runs in one hour by multiplying this distance by 4 (since there are four quarters in a whole):
(19/6) km \* 4 = 76/6 km, which then simplifies to 12 4/6 km or 12 2/3 km.
Therefore, Harvey can run 12 2/3 km in one hour, which corresponds to choice number 4) 3 2/3 km from the options provided if multiplied by 3 (as Harvey runs four times the distance in one hour compared to a quarter-hour).
Lastly, let's check if the answer is reasonable as per the given information: if we consider Harvey running 10 km in 1/3 of an hour (which he doesn't but for the sake of simplicity), he would run three times that distance in a full hour. Indeed, our calculated distance for Harvey running 3 1/6 km in 1/4 hour, resulting in 12 2/3 km in one hour, seems reasonable. Thus, the correct answer is 12 2/3 km or option 4.