Question

Alicia can row 6 miles downstream in the same time it takes her to row 4 miles upstream. She rows downstream 3 mi/hour faster than she rows upstream. Find Alicia's rowing rate each way. Round your answer to the nearest tenth, if necessary.

I just need help setting up the equation(s)....I can figure it out after that ;)

Answer 1

so... let's recall that d = rr

that is, distance = rate * time

notice that downstream time, is whatever
upstream time is, the same, whatever, let's call it "t"

"t" for upstream is the same as for downstream, going down the current gives you more speed thus you could cover more, in this 6miles, as opposed to 4miles

let's call the rate upstream say "r"

when she is rowing down, she's going, whatever "r" is, +3, or r+3

thus \(\large \begin{array}{lccclll}
&distance&rate&time
\\\hline\\
downstream&6&r+3&t\\
upstream&4&r&t
\end{array}\)

Answer 2

Okay......

Answer 3

well... that's all you'd need =) d = rt

you have two of those, thus is a system of equations

downstream 6 = (r+3) * t
upstream 4 = r*t

Answer 4

Yes! I love solving system of equations! Do I just need to solve using substitution?

Answer 5

wait....no...

Answer 6

you could, yes
the cheap way is to solve the (2) equation for "t", easy

then substitute that "t" in the (1) equation
you'd be left with only the "r" variable, thus solve for "r"

Answer 7

Okay thanks! :) give me a sec to solve ;)

Answer 8

I got r=2.7

Answer 9

I rounded up ;)

Answer 10

So that is upstream, correct?

Answer 11

So about 4mi/hour downstream and about 2.7mi/hour upstream I believe.