At 12:00 noon, Isabel started walking east from her house along a staight road at 2 miles per hour. Her sister left the house to go running at 1:00 p.pm, heading south at 8 miles per hour, also along a staight road. Let the house be at the orgin of a coordinate system with north up.
1. Give coordinates of Isabel's position t hours after noon. Give the coordinates of her sister;s position at the same time.
2.Use the distance formula to write an expression for the distance between Isabel and her sister t hours after noon , assuming t1. Simplify the expression.

Question

At 12:00 noon, Isabel started walking east from her house along a staight road at 2 miles per hour. Her sister left the house to go running at 1:00 p.pm, heading south at 8 miles per hour, also along a staight road. Let the house be at the orgin of a coordinate system with north up.
1. Give coordinates of Isabel's position t hours after noon. Give the coordinates of her sister;s position at the same time.
2.Use the distance formula to write an expression for the distance between Isabel and her sister t hours after noon , assuming t>1. Simplify the expression.

jim_thompson5910 · Answer

were you able to get anywhere?

anonymous · Answer

i probabliy could have gotten the second one if i knew how to do the first but not really

jim_thompson5910 · Answer

ok a drawing may help

jim_thompson5910 · Answer

|dw:1366836027599:dw|

anonymous · Answer

so is the coordinate (2t,0)

jim_thompson5910 · Answer

Give coordinates of Isabel's position t hours after noon.

well if t hours have gone by, then she is t*2 = 2t miles east of (0,0)

so the coordinates of Isabel's position t hours after noon is (-2t, 0)

jim_thompson5910 · Answer

oh wow...mixed up my east and west...really bad error...lol

jim_thompson5910 · Answer

i feel dumb lol

but yeah, it's (2t, 0)

anonymous · Answer

lmao its okay

anonymous · Answer

and her sisters is (8t,0) right?

jim_thompson5910 · Answer

Give the coordinates of her sister;s position at the same time.

her position is at (0, -8t) because she's going 8 mph south for t hours

anonymous · Answer

oh okay

jim_thompson5910 · Answer

|dw:1366836324640:dw|

jim_thompson5910 · Answer

for part b, we need to find the distance of that line segment

anonymous · Answer

okay so i set it up like d=$$\sqrt{(2t-(-8t))^2+(0-0))^2}$$

jim_thompson5910 · Answer

no, but you have the right idea though

jim_thompson5910 · Answer

it should be this

$$\large d = \sqrt{(2t-0)^2+(0-8t))^2}$$

then you simplify

anonymous · Answer

okay thanks soooo much lol

jim_thompson5910 · Answer

yw

anonymous · Answer

wait one more thing?

anonymous · Answer

u here?

jim_thompson5910 · Answer

what's your question

anonymous · Answer

when it simplifies it is $$\sqrt{68t^2}$$ right?

jim_thompson5910 · Answer

you can go further

jim_thompson5910 · Answer

$$\large \sqrt{68t^2}$$

$$\large \sqrt{4t^2*17}$$

$$\large \sqrt{4t^2}*\sqrt{17}$$

$$\large 2t\sqrt{17}$$

jim_thompson5910 · Answer

So the distance between them at time t is 

$$\large d = 2t\sqrt{17}$$

anonymous · Answer

then it says find the distance when it is 2 p.m.

jim_thompson5910 · Answer

2 pm is 2 hours away from 12:00 pm noon