Question 43975
Let corbin's location be denoted by A, and Corbin's location denoted by B.
The coordinates of point A at any time "t" are (0,2.5t)
The coordinates of point B at any time "t" are (3t,0)
the distance between the two is the hypotenuse of the right-angled triangle with vertices points A, B and the origin (0,0).
the length of the hypotenuse ("L") can be found using {{{L=sqrt(x^2+y^2)}}}
We can find L using the coordinates of points A and B, by substituting values for x and y:
{{{L=sqrt((3t)^2+(2.5t)^2)}}}
We are looking for L=4
{{{4=sqrt((3t)^2+(2.5t)^2)}}}
squaring:
{{{16=(3t)^2+(2.5t)^2}}}
{{{16=(3t)^2+(2.5t)^2}}}
{{{16=15.25t^2}}}
{{{1.049=t^2}}}
{{{t=1.024hours}}}
if you multiply the decimal (0.024) by 60, the answer is 1 hour and 1 minute; multiplying the decimal remaining by 60 again obtains the full solution: 1 hour, 1 minute, 27seconds