SOLUTION: Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the

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Question 235884: Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two ships leave port at the same time.
One sails south at 15 mi/h and the other sails east at 20 mi/h.
Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.
:
This is right triangle, legs formed by the path of the two ships
distance between the ships is the hypotnenus
a^2 + b^2 = c^2
;
a = 15t
b = 20t
c = d
:
d(t) = sqrt%28%2815t%29%5E2+%2B+%2820t%29%5E2%29
:
d(t) = sqrt%28225t%5E2+%2B+400t%5E2%29
:
d(t) = sqrt%28625t%5E2%29
d(t) = 25t

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The distance for 1st ship is
d%5B1%5D+=+15t
The distance for 2nd ship is
d%5B2%5D+=+20t
The distance between them is
D+=+sqrt%28d%5B1%5D%5E2+%2B+d%5B2%5D%5E2%29
D+=+sqrt%28225t%5E2+%2B+400t%5E2%29
D+=+sqrt%28225+%2B+400%29%2At
D+=+25t
check:
In 10 hours
t+=+10
D+=+25%2A10
D+=+250
d%5B1%5D+=+15%2A10
d%5B1%5D+=+150
d%5B2%5D+=+20%2A10
d%5B2%5D+=+200
D+=+sqrt%28d%5B1%5D%5E2+%2B+d%5B2%5D%5E2%29
D+=+sqrt%28150%5E2+%2B+200%5E2%29
D+=+sqrt%2822500+%2B+40000%29
D+=+sqrt%2862500%29
D+=+250
OK