You are here:

# Algebra/Mathematics/High school

Question

Problem
I canīt resolve the next problem:
An athletics track is to have a perimeter of 400 m and straights of 78.
Find the radius r of the circular 'bend'.
(The problem has the answer: 38.8 m)
I attached the image...
When i thought i finally have the answer is incorrect...

The bend in the track is a semicircle at both ends.
When boht ends are thought of at once, this forms a circle.
This radius around a circle is 2*pi*r.

If we take 78 as the length of a side, and there are two sides, that gives 2*78 = 156 as the side length.  If we then take 400 - 156 = 244, that gives the length left for the ends.

To find the raidus, we know the length of the ends is both 2*pi*r and 244.
Solving 2*pi*r = 244 gives r = 122/pi.  That should give a radius of around 38.8 meters.

To make the track fairly close to exact 400 m in length,
this raidus should be measured as 38.33 meters.
That's 33 cm beyond 38 meters, and it would be really hard to get it down to the mm.

Algebra

Volunteer

#### Scott A Wilson

##### Expertise

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

##### Experience

I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Publications
Documents at Boeing in assistance on the manufacturiing floor.

Education/Credentials
MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.