Question

The two cars are traveling in directions that are at right angle. Let x and y be the distances traveled by the two cars in t hours. Hence

x = 50 t and y = 60 t

Since the two directions are at right angle, Pythagora's theorem can used to find distance D between the two cars as follows:

D = sqrt ( x 2 + y 2 )

We now find the time at which D = 300 miles by solving

sqrt ( x 2 + y 2 ) = 300
Square both sides and substitute x and y by 50 t and 60 t respectively to obtain the equation
(50 t) 2 + (60 t) 2 = 300 2
how to Solve the above equations to obtain
t = 3.84 hours?

Answer 1

well start by collecting like terms on ther left hand side

\[t^2(50^2 + 60^2) = 300^2\]

so

\[t^2 = \frac{300^2}{(50^2 + 60^2)}\]

hopefully you can solve for t, from here.