Problema Solution
Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18 mph, and the other travels due east at a speed of 24 mph. How long until the distance between them is 60 miles?
Answer provided by our tutors
make a drawing
you will notice that the paths of the cyclists are legs of right triangle and the distance between them is the length of the hypotenuse
let t = the time of the travel
the distance that the first cyclist traveled: 18*t miles
the distance that the second cyclist traveled: 24*t miles
using the Pythagorean Theorem we can write
(18t)^2 + (24t)^2 = 60^2
by solving we find and consider the positive root
t = 2 h
click here to see the step by step solution of the equation
it takes 2 hours until the distance between them is 60 miles.