Question 106198

distance(d) equals rate(r) times time(t) or d=rt; r=d/t and t=d/r

Let r=speed (rate) of the river

rate of the boat downstream=25+r
rate of the boat upstream=25-r

Time to travel downstream=(distance downstream)/(rate downstream)=240/(25+r)
Time to travel upstream=(distance upstream)/(rate upstream)=160/(25-r)

Now we are told that these two times are equal. So:

240/(25+r)=160/(25-r)  multiply both sides by (25+r)(25-r)

240(25-r)=160(25+r)  get rid of parens
6000-240r=4000+160r  subtract 6000 and also 160r from both sides

6000-6000-240r-160r=4000-6000+160r-160r  collect like terms

-400r=-2000  divide both sides by -400

r=5 mph-------------------rate (speed) of the river

CK
240/30=160/20
8=8

Hope this helps---ptaylor