Certainly! Let's solve the problem step-by-step.
We are told that the ratios are inversely proportional. When two quantities are inversely proportional, their product is constant. This means if one quantity increases, the other decreases in such a way that their product remains the same.
Given:
- [tex]\( t_1 = 4 \)[/tex]
- [tex]\( s_1 = 5 \)[/tex]
- [tex]\( s_2 = 2 \)[/tex]
We need to find the value of [tex]\( t_2 \)[/tex].
Since the ratios are inversely proportional, we can write the relationship as:
[tex]\[ t_1 \cdot s_1 = t_2 \cdot s_2 \][/tex]
Substitute the given values into the equation:
[tex]\[ 4 \cdot 5 = t_2 \cdot 2 \][/tex]
Simplify the left-hand side of the equation:
[tex]\[ 20 = t_2 \cdot 2 \][/tex]
Next, solve for [tex]\( t_2 \)[/tex] by dividing both sides of the equation by 2:
[tex]\[ t_2 = \frac{20}{2} \][/tex]
Calculate the division:
[tex]\[ t_2 = 10 \][/tex]
So, the value of [tex]\( t_2 \)[/tex] is [tex]\( 10 \)[/tex].
