SOLUTION: Hi! I am having difficulty trying to figure this problem out. Any help or direction that you are able to provide in solving is most appreciated! Two ships leave port at the sa

Question 38279: Hi! I am having difficulty trying to figure this problem out. Any help or direction that you are able to provide in solving is most appreciated!
Two ships leave port at the same time. Ship A sails north at a speed of 20mph while ship B sails east at a speed of 30mph.
a.- Find an expression in terms of the time 't'(in hours) giving the distance between the two ships.
b.- Using the expression obtained in part (a), find the distance between the two ships 2hr after leaving port.
Found 2 solutions by fractalier, checkley71:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Make a right triangle diagram, with one leg going north (y) and one going east (x). Label the hypotenuse z.
In general D = RT, distance = rate*time, so we can write
y = 20t and x = 30t
Now from the Pythagorean Theorem, we know
z^2 = x^2 + y^2
So let us substitute
z^2 = (30t)^2 + (20t)^2
z^2 = 900t^2 + 400t^2
z^2 = 1300t^2
z = sqrt(1300t^2)
z = 10t*sqrt(13)
and we're done with part a...
In part b, t = 10, so
z = 10*10*sqrt(13)
z = 100*sqrt(13)
z = 360.6 mi
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
LET D BE THE DISTANCE BETWEEN THE 2 SHIPS & BWCAUSE THIS PROBLEM CAN BE REPRESENTED BY A RIGHT (90 DEGREE)TRIANGLE THEN A~2+B~2=D~2 SO
20~2+30~2=D~2 OR 400+900=D~2 OR 1300=D~2 OR D=SQRT1300 OR D=36.06 MILES AFTER 1 HOUR.
2 HOURS AFTER THEY LEAVE THEY ARE D~2=(2*20)~2+(2*30)~2 OR D~2=40~2+60~2 OR
D~2=1600+3600 OR D~2=5200 OR D=SQRT5200 OR D=72.11 MILES APART

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