Sophie jogs four and one-fourth miles in seven-eighths hour. How far would she run in four and one-half hours if she kept the same pace?
4.25mi/0.875hr * 4.5hr = 21.86 mi
or, using fractions
(17/4 mi)/(7/8 hr) * (9/2 hr)
= 17/4 * 8/7 * 9/2 = 153/7 = 21 6/7 mi
To find out how far Sophie would run in four and one-half (4.5) hours, we can use the concept of proportions.
First, let's determine Sophie's average speed in miles per hour during her original jog.
Sophie jogs four and one-fourth (4 1/4) miles in seven-eighths (7/8) hour.
To find her average speed, we divide the distance by the time taken:
Average speed (in mph) = distance (in miles) / time (in hours)
Average speed = 4 1/4 / 7/8
To simplify this division, we can convert the mixed number (4 1/4) into an improper fraction:
4 1/4 = (4 * 4 + 1) / 4 = 17/4
So, her average speed is:
Average speed = 17/4 / 7/8
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Average speed = (17/4) * (8/7) = 34/1 = 34 mph
Now that we know her average speed, we can calculate the distance she would run in 4.5 hours using the formula:
Distance = Speed * Time
Distance = 34 mph * 4.5 hours
Multiplying these values gives us:
Distance = 153 miles
Therefore, if Sophie keeps the same pace, she would run 153 miles in four and one-half hours.
To find out how far Sophie would run in four and a half hours, we can use a proportion.
First, let's calculate Sophie's running speed:
Distance: 4 and 1/4 miles
Time: 7/8 hour
To find the speed, we divide the distance by the time:
Speed = Distance / Time = (17/4) miles / (7/8) hour
To simplify this division, we can multiply the numerator by the reciprocal of the denominator:
Speed = (17/4) miles * (8/7) hour
Now, let's find out how far she would run in 4 and 1/2 hours:
Distance = Speed * Time = (17/4) miles * (8/7) hour * (9/2) hours
To simplify this calculation, we can cancel out common factors:
Distance = (17 * 8 * 9) / (4 * 7 * 2) miles
Multiply the numerator and denominator:
Distance = 1224 / 56 miles
Simplify the fraction:
Distance = 21.8571428571 miles
So, Sophie would run approximately 21.86 miles in four and a half hours if she kept the same pace.