Question 537024: At 1:00P.M., ship A is 30mi due south of ship B and sailing north at a rate of 15mi/hr. if ship B is sailing west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! At 1:00P.M., ship A is 30mi due south of ship B and sailing north at a rate of 15mi/hr. if ship B is sailing west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal.
:
We can solve this as a right triangle
let t = travel time of both ships
then
15t = distance traveled by ship A
however, it is traveling toward the point of reference, therefore we write it
(30-15t)
and
10t = distance traveled by ship B, away from the point of reverence
:
Let d = distance between the ships at t time, (the hypotenuse of the right triangle)
:
d = 
FOIL and combine like terms
d = 
:
d = 
we can find the axis of symmetry, disregarding the radical sign
a=325, b=-900
t = 
t = 
t = 1.3846 hrs, travel time for minimum distance
:
Find the minimum distance
d = 
d = 
d = 
d = 
d = 
d = 16.64 mi apart after 1.3846 hrs, minimum distance between the ships
:
Find the time this occurs
Change 1.3846 to: 1 hr + .3846(60) = 1 hr 23 min
1:00 + 1:23 = 2:23 PM
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