Fred is training for a cross-country race. At practice last week, he ran 6.25 miles in 1
1
4
hours. At that speed, how long would it take Fred to run 8.5 miles?
To find out how long it would take Fred to run 8.5 miles, we need to determine the running speed per hour.
First, we need to find the time it took Fred to run 6.25 miles: 1 1/4 hours = 1.25 hours.
Next, we need to find Fred's speed in miles per hour: 6.25 miles / 1.25 hours = 5 miles per hour.
Finally, we need to calculate the time it would take Fred to run 8.5 miles: 8.5 miles / 5 miles per hour = 1.7 hours.
Therefore, it would take Fred 1.7 hours to run 8.5 miles.
To calculate how long it would take Fred to run 8.5 miles at the same speed, we can use the concept of proportions.
Let's set up a proportion by comparing the distance and time:
Distance 1 / Time 1 = Distance 2 / Time 2
In this case:
Distance 1 = 6.25 miles
Time 1 = 1 1/4 hours (which can be written as 5/4 hours)
Distance 2 = 8.5 miles
Time 2 = unknown
Now we can plug in the values we know:
6.25 miles / 5/4 hours = 8.5 miles / Time 2
To find Time 2, we can solve for it algebraically:
(6.25 miles * Time 2) = (5/4 hours) * 8.5 miles
Divide both sides by 6.25 miles:
Time 2 = (5/4 hours * 8.5 miles) / 6.25 miles
Now we can calculate Time 2:
Time 2 = (5/4) * 8.5 / 6.25
Time 2 = 42.5 / 25
Time 2 = 1.7 hours
Therefore, it would take Fred approximately 1.7 hours to run 8.5 miles at the same speed.