Question 975138
r, boat if no current
c, current
d, distance each way
t, total time up and back


RT=D basic uniform rates travel relationship



__________________speed__________time__________distance
UP________________r-c____________d/(r-c)___________d
BK________________r+c____________d/(r+c)___________d
Total____________________________t____________2d


UNKNOWN VARIABLES:  r
KNOWN:  c, t, d.


{{{highlight_green(d/(r-c)+d/(r+c)=t)}}}, and you want to solve for r.


{{{d(r+c)+d(r-c)=t(r-c)(r+c)}}}
{{{dr+cd+dr-dc=t(r^2-c^2)}}}
{{{2dr=tr^2-tc^2}}}
{{{tr^2-2dr-tc^2=0}}}
You might expect that as an academic exercise, that the trinomial may be factorable, but staying completely in symbols,


{{{r=(2d+- sqrt(4d^2+4t*tc^2))/(2t)}}}


{{{r=(2d+- 2sqrt(d^2+t^2c^2))/(2t)}}}


{{{highlight(r=(d+- sqrt(d^2+(tc)^2))/t)}}}
You would want the PLUS form.  Substitute the given values for d, t, c, and evaluate r.