Leslie ran 4 1/2 laps around the park in 3/4 hour. Kayla ran 3 1/2 laps around the same park in the same amount of time. How many more laps around the park can Leslie run in 1 hour than Kayla at these rates? PLZ EXPLAIN THE STEPS SO I CAN UNDERSTAND ALSO! :D
To find out how many more laps around the park Leslie can run in 1 hour than Kayla, we need to first determine how many laps each of them runs in 1 hour.
We know that Leslie ran 4 1/2 laps in 3/4 hour. To find out how many laps Leslie can run in 1 hour, we'll set up a proportion:
(4 1/2 laps) / (3/4 hour) = (x laps) / (1 hour)
To solve for x, we can cross-multiply:
(4 1/2 laps) * (1 hour) = (3/4 hour) * (x laps)
Multiply the fractions:
9/2 laps = (3/4) * (x laps)
Now, let's solve for x. We can divide both sides of the equation by 3/4:
(9/2 laps) / (3/4) = x laps
To divide fractions, we multiply by the reciprocal:
(9/2 laps) * (4/3) = x laps
Multiply the fractions:
36/6 laps = x laps
Simplify the fraction:
6 laps = x laps
So, Leslie can run 6 laps around the park in 1 hour.
Now, let's follow the same steps to determine how many laps Kayla can run in 1 hour. We know that Kayla ran 3 1/2 laps in 3/4 hour.
(3 1/2 laps) / (3/4 hour) = (x laps) / (1 hour)
Cross-multiply:
(3 1/2 laps) * (1 hour) = (3/4 hour) * (x laps)
Multiply the fractions:
7/2 laps = (3/4) * (x laps)
Divide both sides by 3/4:
(7/2 laps) / (3/4) = x laps
Multiply by the reciprocal:
(7/2 laps) * (4/3) = x laps
Multiply the fractions:
28/6 laps = x laps
Simplify the fraction:
4 2/3 laps = x laps
So, Kayla can run 4 2/3 laps around the park in 1 hour.
To find how many more laps Leslie can run than Kayla, we subtract the number of laps Kayla can run from the number of laps Leslie can run:
6 laps - 4 2/3 laps = (6 laps) - (14/3 laps)
To subtract mixed numbers, we need to convert the mixed number to an improper fraction. Multiply the whole number by the denominator and add the numerator:
6 laps - 14/3 laps = 18/3 laps - 14/3 laps
Subtract the fractions:
(18/3 - 14/3) laps = 4/3 laps
So, Leslie can run 4/3 laps more than Kayla in 1 hour.
Leslie:
4.5 laps = 0.75 hrs
x laps = 1.00 hrs
Find x (the number of laps Leslie does in an hour)
Kayla
3.5 laps = 0.75 hrs
y laps = 1.00 hrs
Find y (the number of laps Kayla does in an hour)
x - y is the difference or extra that Leslie will run in an hour
Leslie: 4.5Laps/0.75h = 6 Laps/h
Kala: 3.5Laps/0.75h = 4.67 Laps/h
6Laps/h - 4.67Laps/h = 1.33 Laps/h.
Therefore, Leslie can run 1.33 more laps
in 1 hr. than Kayla.