A circular race track is being built. The outsidediameter of the track is 200 feet, and the inside diameter is 180 feet. If two runners run around the track once, with one of them running on the outside edge of the track, while the other is running on the inside edge, how much further will the outside runner have to run?
circumference = 2 pi r
2 pi (100 - 90)
= 20 pi
= 20 * 3.14159 approximately
where did 100 and 90 come from
d1 = pi*2r = 3.14*200 = 628 Ft.
d2 = pi*2r = 3.14*180 = 565 Ft.
d1-d2 = 628-565 = 63 Ft.
this question is also referring to the question above:
Referring to the runners in the preceding problem, if the runners both run at a speed of 6 miles per hour, how much time will elapse between the first runner finishing and the second runner finishing. Assume they start at the same time.
d1 = (628/5280) * 1mi = 0.119 mi
d2 = (565/5280) * 1 mi = 0.107 mi.
V1*T1 = 0.119
6T1 = 0.119
T1 = 0.0198 h = 1.19 min.
V2*T2 = 0.107
6T2 = 0.107
T2 =
T = T1-T2 =
To find out how much further the outside runner will have to run, we need to calculate the circumference of each circle.
The formula to calculate the circumference of a circle is:
Circumference = π × diameter
Let's start by calculating the circumference of the outside track:
Circumference of outside track = π × diameter of outside track
= π × 200 feet
= 628.32 feet (approximately)
Next, let's calculate the circumference of the inside track:
Circumference of inside track = π × diameter of inside track
= π × 180 feet
= 565.48 feet (approximately)
Now, we can find the difference in distances by subtracting the circumference of the inside track from the circumference of the outside track:
Difference in distances = Circumference of outside track - Circumference of inside track
= 628.32 feet - 565.48 feet
= 62.84 feet (approximately)
Therefore, the outside runner will have to run approximately 62.84 feet further than the inside runner.