
Lines in a Plane 15
You are driving from point A(24,96) on a map grid towards point B with a velocity defined by d=(85,65) km/h
a) state the parametric eqtns of the highway line.
b) how long have you been traveling when you reach a point P 102 km east of where you started at point A?
c) what are the coordinates of your position P at that time?
so this is my work below, I need help with parts b and c.
a) x=24+85t
y=9665t
b) d=AB
(85,65)=(x24)(y96)
x24=85
x=109
y96=65
y=31
AB=sqrt (11450)
(11450)^ (0.5) +102 = 209
d/s=t
209/(65/85)=273 h
The answer in the back is 55 min
c) P(194,34)
Their answer is (102, 36.4)
How do I get their answers and what did I do wrong?

$\displaystyle x=24+85t$
Since we are due east, we can use x=102.
$\displaystyle 102=24+85t$
$\displaystyle t=.917647$
This is hours. Multiply by 60 and get 55.05 minutes.
part c, y=9665(.917647)=36.35
The coordinates are (102, 36.35)
I think you just had a small mental block. You have the right equations.