Certainly! Let's break down the problem and find the constants of proportionality along with their relationship.
Given:
- An albatross can fly 400 kilometers in 8 hours at a constant speed.
- The equation representing this situation is [tex]\( d = 50t \)[/tex], where [tex]\( d \)[/tex] is the distance in kilometers and [tex]\( t \)[/tex] is the number of hours.
1. Two Constants of Proportionality:
- Speed of the albatross:
The speed can be derived from the distance-time relationship. According to the equation [tex]\( d = 50t \)[/tex], where speed is defined as the distance traveled per unit time.
So, speed [tex]\( s \)[/tex] is [tex]\( 50 \)[/tex] kilometers per hour.
- Inverse of the Speed:
The inverse of the speed is also a constant of proportionality. This represents the time taken to cover one kilometer. We can compute it as follows:
[tex]\[
\frac{1}{\text{speed}} = \frac{1}{50} \text{ hours per kilometer}
~~~ \text {or ~} 0.02 \text{ hours per kilometer}
\][/tex]
2. Relationship Between These Two Values:
- The speed [tex]\( s \)[/tex] is [tex]\( 50 \)[/tex] kilometers per hour.
- The inverse of this speed, which is [tex]\( \frac{1}{s} \)[/tex], is [tex]\( \frac{1}{50} = 0.02 \)[/tex] hours per kilometer.
The relationship between these two values is that speed and its inverse are reciprocal of each other. This means that:
[tex]\[
50 \times 0.02 = 1
\][/tex]
Hence, if you multiply the speed by its inverse, the product is always 1. This indicates that they are indeed reciprocal values.
In conclusion:
- The two constants of proportionality are [tex]\( 50 \)[/tex] kilometers per hour and [tex]\( 0.02 \)[/tex] hours per kilometer.
- These two values are in a reciprocal relationship, meaning that each is the inverse of the other.
