Question

Joe is driving west at 60 km/h and Dave is driving south at 70 km/h. Both cars are approaching the intersection of the 2 roads. At what rate is the distance between the cars decreasing when Joe's car is 0.4 km and Dave's is 0.3 km from the intersection.

Answer 1

oooh i bet they are \(.5\) miles apart then right?

Answer 2

ok so i did this the way my teach taught me

Answer 3

what i did was 60 times 0.4 for joe and 70*0.3 for dave

Answer 4

you want \(d'\) and you know
\[x^2+y^2=d^2\]
differentiate get \[2xx'+2yy'=2dd'\] or
\[xx'+yy'=dd'\] you know all the numbers you need to solve this for \(d'\)

Answer 5

for that 24(60)+70(21)=sqrt1017 dy/dt

Answer 6

\[x'=60,y'=70,x=.4,y=.3,d=.5\]

Answer 7

you lost me there with the square root

Answer 8

you are given all the numbers you need to solve this equation \[xx'+yy'=dd'\] for \(d'\) which is what you are looking for

Answer 9

well didnt i have to find d?

Answer 10

well, you are not told \(d\) but you can find it with pythagoras

Answer 11

yes i did that and got 31.89

Answer 12

ooh no

Answer 13

there is a very simple geometric solution if youd like to see that

Answer 14

\[\sqrt{.3^2+.4^2}=.5\]

Answer 15

it is the world famous 3 - 4 - 5 mother of all right triangles

Answer 16

wait so their are two trianlges to this question ?

Answer 17

no only one

Answer 18

why cant i times 0.4 to 60 ?

Answer 19

i was looking at my notes and the teacher did the similar way

Answer 20

you are told how far away they are from the intersection right? you don't need to calculate it, you are told
one is .3, the other is .4, so the distance between them is .5

Answer 21

no doubt your teacher did a problem where you had to calculate how far they had gone, but in this case is it different
you don't need to find how far they have gone, you are told how far they are from the intersection

Answer 22

the problem i am refering too is somthing like " man goes south lady goes north , wahts the distance 2 mins later" so these tyoes are different ?

Answer 23

yeah because in that one they are moving away from each other so you would need to find out how far they had gone

Answer 24

so i did what u told me 21(70)+24(60)=0.5dx/dt? right?

Answer 25

no lets go slow

Answer 26

you do not need to find x, you are told x, x is .3
you do not need to find y, you are told y, y is .4

Answer 27

ok

Answer 28

\[70\times .3+60\times .4=.5d'\]

Answer 29

i hope i got them in the right order, i forget
check that it is right, the .3 goes with the 70 and the .4 with the 60 not the other way around

Answer 30

yeah that is right

Answer 31

dammnn thank you so much

Answer 32

do u hate it when the notes dont match the HW and u get stuck ?