Question

Juan and his little brother Miquel ran around a circular track together. Juan ran on the inner track, which has a radius of 30 feet. Miquel ran on the outer track which has a radius of 40 feet. How much further did Miquel run than Juan after two loops around the track? A. 31.4 ft. B. 62.8 ft. C. 125.6 ft. D. 219.8 ft.

Answer 1

C

Explanation:

Mathematically, to calculate the distance run around the tracks, we need to know the circumferences of the tracks

The circumference of a circle is 2 π r

For the 40 feet track, circumference will be 2 * π * 40 = 80 π feet

In two loops, distance ran will be 2 * 80 π feet = 160 π feet

For the 30 feet track , circumference will be 2 * π * 30 = 60 π feet

In two loops, distance will be 2 * 60 π = 120 π feet

Thus, how much further Miguel ran will be the difference between the two loops

= 160 π - 120 π = 40 π feet

The distance here here if we substitute for π will be 40 * 22/7 = 125.71 ft

The closer answer to this is option C

Answer 2

Explanation:

Using the formula for finding the circumference of a circle expressed as:

`C= 2\pi r` where:

r is the radius of the circular track

If Juan ran on the inner track, which has a radius of 30 feet, the area of the trach is expressed as:

`C_i= 2\pi (30)\\C_i = 60\pi ft`

If Miquel ran on the outer track which has a radius of 40 feet, the area of the outer track will be expressed as:

`C_o= 2\pi (40)\\C_o = 80\pi ft\\`

To know how much further did Miquel run than Juan after two loops around the track, we will take the difference in the circumference as shown:

`C = C_o - C_i\\C = 80\pi - 60\pi\\C = 20\pi\\C = 20(3.14)\\C = 62.8ft\\C = 2(62.8)\\C = 125.6 feet \\`

Hence Miguel has ran 125.6 ft further after two loops around the track