Answer:
76 mi/h
Explanation:
[tex]\frac{da}{dt}[/tex] = Velocity of car A = 50 mi/h
a = Distance car A travels = 40 mi
[tex]\frac{db}{dt}[/tex] = Velocity of car B = 60 mi/h
b = Distance car B = 30 mi
c = Distance between A and B after 3 hours = √(a²+b²) = √(40²+90²) = 50 mi
From Pythagoras theorem
a²+b² = c²
Now, differentiating with respect to time
[tex]2a\frac{da}{dt}+2b\frac{db}{dt}=2c\frac{dc}{dt}\\\Rightarrow a\frac{da}{dt}+b\frac{db}{dt}=c\frac{dc}{dt}\\\Rightarrow \frac{dc}{dt}=\frac{a\frac{da}{dt}+b\frac{db}{dt}}{c}\\\Rightarrow \frac{dc}{dt}=\frac{40\times 50+30\times 60}{50}\\\Rightarrow \frac{dc}{dt}=76\ mi/h[/tex]
∴ Rate at which distance between the cars is increasing is 76 mi/h
The cars are getting farther apart at this time
