Question

Two cars leave a store at the same time. One goes north, driving at a speed 20 kph slower than the car going east. After 12 minutes, the cars are 20 kilometers apart from each other. What is the average speed of each car?

Answer 1

your pic will look like this:

Answer 2

Now we have to figure in the time of 12 minutes. First of all, your problem is in hours, not minutes, so we need to convert 12 minutes to hours. A very small decimal point. Can you do that?

Answer 3

12 minutes = .2 hours

Answer 4

Good! Now, since thee distnce formula says that distance = rate * time, we have the rates in our pics, now we need to multiply in our time of .2, like this:

Answer 5

distribute the .2 into the parenthesis. What do you get for that one?

Answer 6

?

Answer 7

yes, that's right! Now we need to use all those in the Pythagorean theorem. Can you set that up do you think?

Answer 8

i know the formula is \[c = \sqrt{a^2 + b^2}\] but i don't know which one goes where

Answer 9

let me work it out and then I will post for you, ok? Using the quadratic formula right now...

Answer 10

thank you so much

Answer 11

you bet!

Answer 12

ok, the equation you get when you put all that into pythagorean's theorem is this:

Answer 13

\[(.2r-4)^{2}+(.2r)^{2}=(20)^{2}\]which after a long and hideous process comes out to be this polynomial:

Answer 14

\[.08r ^{2}-1.6r-384=0\]What I did for that was just to expand all my parenthesis in the pythagoreans theorem and then move everything to the same side in order to factor.

Answer 15

That I factored with the quadratic formula and it looks like this:\[\frac{ 1.6\pm \sqrt{2.56-4(.08)(-384)} }{ .16 }\]When you do all that math you get these factors:
(x-80)(x+60)=0

Answer 16

solving those for x you get that x = 80 and x = -60. Well in our case the x's are supposed to be r's cuz we are dealing with the rates of the drivers, right?

Answer 17

If r = -60, we can't use that one because everyone knows that speed is not a negative value, so r = 80.

Answer 18

Fill in our "r"s in our triangle to find the rates of each driver.

Answer 19

That's in kilometers per hour, dear.

Answer 20

And that's it in a nutshell, and I am going to bed! ; )

Answer 21

so the average speed of each car is 60 kph and 80 kph?

Answer 22

thank you very very much

Answer 23

yep! You got it!