Question 707037
Distance between ships: At noon,
 Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour.
 Ship B is sailing east at a rate of 6 miles per hour.
 Write the distance (d) between ships as a function of the time (t), where t=0 represents noon.
:
The is a Pythagoras problem; d = {{{sqrt(a^2+b^2)}}} where:
a = 6t (distance east)
b = (45-8t); distance north
d = distance between the two ships
:
Ref point, is the starting point of b when t=0 they are 45 mi apart
d = {{{sqrt((6t)^2 + (45-8t)^2)}}}
FOIL (45-8t)(45-8t)
d = {{{sqrt(36t^2 + 2025-720t+64t^2)}}}
combine like terms
d = {{{sqrt(100t^2-720t+2025)}}}
:
Graphically, time on the x axis, distance on the y axis
{{{ graph( 300, 200, -10, 20, -20, 200, sqrt(100x^2-720x+2025), 107) }}}
You can see after 14 hrs, they are about 107 mi apart (green line)