Question

Jane is running on a circular track with a radius of 50 yards. A mile is 1760 yards. What is the least number of complete laps she must run to cover a distance of at least 4 miles?​

Answer 1

18

Explanation:

Half of 4 times 9=18

Answer 2

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:

`C = 2 \pi r`

Where, "C" is the circumference and "r" is the radius

`C = 2 * 3.14 * 50 = 314`

Thus one lap is equal to 314 yards

Convert yards to miles

Given that,

1 mile = 1760 yards

`1 \text{ yard } = (1)/(1760) \text{ miles }`

Therefore, 314 yards is equal to,

`314 \text{ yards } = (1)/(1760) * 314 \text{ miles } = 0.1784 \text{ miles }`

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

`4 * 1 = x * 0.1784\\\\x = (4)/(0.1784)\\\\x = 22.42 \approx 22`

Thus she needs to run 22 laps to cover 4 miles