Jane needs to run 22 laps to cover 4 miles
Solution:
From given question,
Jane is running on a circular track with a radius of 50 yards
Radius = 50 yards
The total distance covered in 1 lap is equal to circumference of circular track
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where, "C" is the circumference and "r" is the radius
[tex]C = 2 \times 3.14 \times 50 = 314[/tex]
Thus one lap is equal to 314 yards
Convert yards to miles
Given that,
1 mile = 1760 yards
[tex]1 \text{ yard } = \frac{1}{1760} \text{ miles }[/tex]
Therefore, 314 yards is equal to,
[tex]314 \text{ yards } = \frac{1}{1760} \times 314 \text{ miles } = 0.1784 \text{ miles }[/tex]
What is the least number of complete laps she must run to cover a distance of at least 4 miles?
In 1 lap, she covers 0.1784 miles
Let "x" be the number of laps needed to cover 4 miles
Therefore,
1 lap = 0.1784 miles
x lap = 4 miles
This forms a proportion and we can solve the sum by cross multiplying
[tex]4 \times 1 = x \times 0.1784\\\\x = \frac{4}{0.1784}\\\\x = 22.42 \approx 22[/tex]
Thus she needs to run 22 laps to cover 4 miles
