The value of the constant of variation is 2,199 feet. The speed of the another rider is 87.96 feet/sec.
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
A.) The time it takes to complete a go-cart course is inversely proportional to the average speed of the go-cart. Therefore, the relationship can be written as,
Average speed ∝ (1/time)
Now, if the constant of variation is introduced then the relationship can be written as,
Average speed = k(1/time)
Substituting the values, we will get,
[tex]73.3\frac{ feet}{second}= k \times \dfrac{1}{30\ seconds}\\\\73.3 \frac{ feet}{second}\times 30\ seconds = k\\\\k = 2,199\ feet[/tex]
Hence, the value of the constant of variation is 2,199 feet.
B.) The speed of the another rider is,
Average speed = k(1/time)
Average speed = 2,199×(1/25) feet/sec
Average speed = 87.96 feet/sec
Hence, the speed of another rider is 87.96 feet/sec.
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