Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.
Step-by-step explanation:
Given the speed of boat = 1200 mph
the speed of steamer =500 mph
Distance traveled by boat in time "t"=[tex]\frac{distance}{time}=\frac{1200}{t}[/tex]
Distance traveled by steamer in time time "t"=[tex]\frac{500}{t}[/tex]
As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)
By Pythagoras theorem
[tex](Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow(\frac{1200}{t})^2+(\frac{500}{t})^2=(1300)^2\\\\\Rightarrow\frac{1440000}{t^2}+\frac{250000}{t^2}=1690000\\\\\Rightarrow\frac{1690000}{t^2}=1690000\\\\\Rightarrow\ t^2=\frac{1690000}{1690000}=1[/tex]
⇒t=1 hour
Thus, after t= 1 hour the distance between them be 1300 mi.
