Answer:
[tex]\frac{16}{9}[/tex] hours
Step-by-step explanation:
Whenever 2 quantities (suppose a and b) are inversely proportional to each other, we can write an proportionality equation (with k as proportional constant) as:
[tex]a=\frac{k}{b}[/tex]
Since, here t is INVERSELY PROPORTIONAL to r, we can say:
[tex]t=\frac{k}{r}[/tex]
Firstly, we have t = 2 hour and r = 40 mph, so we find k:
[tex]t=\frac{k}{r}\\2=\frac{k}{40}\\k=2*40\\k=80[/tex]
Now, secondly, we have r = 45 and k = 80, we need to find t:
[tex]t=\frac{80}{45}\\t=\frac{16}{9}[/tex]
So, it would take [tex]\frac{16}{9}[/tex] hours
