SOLUTION: The circumference of one wheel is 20m longer than of another wheel. The product of the 2 circumferences is 144300mm. Calculate the length of the 2 circumferences.

Question 1003124: The circumference of one wheel is 20m longer than of another wheel. The product of the 2 circumferences is 144300mm. Calculate the length of the 2 circumferences.
Found 2 solutions by jkc52, Theo:
Answer by jkc52(5) (Show Source): You can put this solution on YOUR website!
as a first attempt students use the expressions for circumference.
*****the circumference of a circle with d as diameter is c=pi*d*****
given that c1=c2+20
and
c1*c2=144300 mm^2
therefore
(c2+20)*c2=144300
hence c2^2+20*c2-144300=0
this is a quadratic equation in c2 and can be solved using the standard
procedure
as c2=(-20+760)/2=370 or
c2=(-20-760)/2=-390
as the second answer for c2 is redundant c2=370mm and c1=390mm

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the circumference of one of the wheels = c meters.

the circumference of the other wheel = c + 20 meters.

since both wheels are measured in meters, then the product will be in square meters.

the product, however, is in square millimeters.

it needs to be converted to square meters.

since 1 square millimeter is equal to 1 square meter / 1,000,000, then 144300 square millimters is equal to 144300 square millimmeters / 1,000,000 = .1443 square meters.

you get c * (c + 20) = .1443 square meters.

simplify to get c^2 + 20c = .1443 square meters.

subtract .1443 from both sides of the equation to get:

c^2 + 20c - .1443 = 0

solve this quadratic to get:

c = -20.0072124 meters or c = .0072124 meters

since c can't be negative, c must be equal to .0072124 meters

if c = .0072124 meters, then c + 20 = 20.0072124 meters

.0072124 meters * 20.0072124 meters = .1443 square meters.

this agrees with what the product should be, so c must be a good solution.

if you wanted to convert everything back to millimeters and square millimeters, you would then do the following.

.0072124 meters * 1000 = 7.2124 millimeters.

.0072124 meters * 1000 = 20007.2124 millimeters.

7.2124 millimeters * 20007.2124 millimeters = 144300.0187 square millimeters.

the difference between that and 144300 square millimeters is in the rounding.

what's shown as .0072124 meters is really 0.0072123990649864 meters rounded to 7 decimal digits.

if you use the numbers before they were rounded, you should get much closer to 144300.

i did and i got 144300 exactly.

if you have the capability, the recommendation is alwsys to use the unrounded numbers for all intermediate operations and then round for the final result only.

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