i need to know the answer to this
suppose x varies directly as r, and x varies inversely as t. find t when r equals 10 and x equals -5, if t equals 20 when x equals 4 and r equals 2

- anonymous

- chestercat

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- amistre64

So we are given this:
x = r/t

- amistre64

or really:
x = kr/t where k is any constant, but lets make that constant a "1" for simplicities sake :)

- amistre64

t = r/x then:
t = 10/-5

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## More answers

- amistre64

r = x/t
r = 4/20

- anonymous

its not rate over time. i need to find t!

- amistre64

ack!! r = xt lol i forgot how to multiply :)

- amistre64

r = 4(20)

- amistre64

i see i forgot how to read the question as well..... let me start over :)

- amistre64

Find t when r=10 and x= -5, if t=20 when x= 4 and r=2 whats this mean?

- anonymous

its a variation function

- amistre64

are you looking for the Constant? or what?

- amistre64

4 = k(2/20)
40 = k
x = 40r/t

- anonymous

just finding the answer for t

- anonymous

?

- anonymous

alright, hold on a minute and I will help, I just need to refresh my memory.

- anonymous

First you need to set up a proportion. Since x varies directly as r and inversely as t, it will look like this:\[x_{1}t _{1} / r _{1} = x _{2}r _{2} / r _{2}\]

- anonymous

You plug in your values, which would make
\[(4)(20) / 2 = 5(t)/10\]

- anonymous

or, 80 / 2 = 5t/10.

- anonymous

you then solve the proportion by cross multiplying, like so:
\[(80)(10) = 2(5t)\]

- anonymous

or, 800 = 10t ; solving the equation leaves you with t = 80.

- anonymous

hope that helps! ^-^

- amistre64

-5 i think it was :) which makes it -80 right?

- anonymous

ah true, thanks for pointing that out, I always get my signs messed up

- amistre64

t = 400/-5 = -80

- amistre64

i was just wondering if i did it right.... :)

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