Question

Avery can run at 10 uph (units per hour). The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does Avery need to reach the river?

Answer 1

@satellite73

Answer 2

you are looking for the distance from \(4x+3y=12\) to \((7,5)\)

Answer 3

yes

Answer 4

should i set up a parametric?

Answer 5

dont think it is necessary

Answer 6

you could use calc if you want, that is one way

Answer 7

Do you mean use calculus? If so, I don't know much about it :(

Answer 8

oh then you cant use it
you have to do something else

Answer 9

the slope of the line is what?

Answer 10

Can I find the line that is perpendicular to 4x+ 3y = 12 and also goes through the point (7, 5)? Then find the intersection of the two lines.

Answer 11

And after I find the intersection I can find the distance between (7, 5). But how do I find the time from there?

Answer 12

exactly

Answer 13

the time?

Answer 14

whatever it is time is distance divided by rate

Answer 15

It asks how much time it takes for her to reach the river

Answer 16

The rate would be the slope of the perpendicular line right?

Answer 17

that is a red herring, something to do at the end to keep busy

Answer 18

no the rate is teh rate

Answer 19

you are told the rate is 10

Answer 20

Oh I misread that. My bad.

Answer 21

find the distance, divide by 10 to find the time

Answer 22

OK I am doing that right now. Please give me a moment

Answer 23

ok

Answer 24

calculus may be easier...

Answer 25

Yeah but I'll get to that maybe in the next year or so :)

Answer 26

So far I am taking accelerated geometry

Answer 27

seems pretty speedy to me

Answer 28

Haha..

Answer 29

Have you finished solving this problem? Hope so. If not, what have you left to do?

Answer 30

I get the Point of Intersection as (2.04, 1.28)

Answer 31

Is that correct?

Answer 32

ikd i didn't do it
want me to check?

Answer 33

I would truly appreciate it if you can

Answer 34

ok give me a minute

Answer 35

There is a formula for finding the distance from a point to a line; do you recall having seen such a formula before? I've forgotten which course you're in.

Answer 36

\(\large D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Answer 37

i get \[-3 x + 4 y =-1\] for the other line

Answer 38

Yes in slope-int form I get: y = (3/4)x - 1/4

Answer 39

I get my final answer to be 0.62 hours

Answer 40

that is what i got as well

Answer 41

distance \(6.2\) divide by 10

Answer 42

Thank you! Do you still have some more time to help me out?

Answer 43

sure