SOLUTION: Two cars leave at noon from the same point, one traveling east at 50 mph, the other traveling due north at 60 mph. (a) How far apart are they at 1 PM? at 1:30 PM? (b) If t is the

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Question 80314: Two cars leave at noon from the same point, one traveling east at 50 mph, the other traveling due north at 60 mph.
(a) How far apart are they at 1 PM? at 1:30 PM?
(b) If t is the number of hours after noon, find an equation expressing the distance between the cars as a function of t.
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
(50T)^2+(60T)^2=DISTANCE ^2
@ 1:00 THEY ARE
(50*1)^2+(60*1)^2=D^2
5062=60^2=D62
2500+3600=D^2
D^2=5100
D=SQRT5100
D=71.414 MILES APART @ 1:00.
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@ 1:30 THEY WILL BE:
(50*1.5)^2+(60*1.5)^2=D^2
75^2+90^2=D^2
D^2=5625+8100
D^2=13725
D=117.154 MILES APART @ 1:30.
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FORMULA IN TERMS OF T IS:
(S1T)^2+(S2T)^2=D^2
T^2(S1^2+S2^2)=D^2
T^2=D^2/(S1^2+S2^2)
T=(D/SQRT(S1^2+S2^2)