Question 766346
a riverboat for tourists averages 12 mph in still water. It takes the boat 1hour and 4 minutes to go 6 miles upstream and return. find the rate of the current
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let c=rate of current
12+c=rate of boat downstream
12-c=rate of boat upstream
1hour and 4 min=1+1/15=(16/15) hour
travel time=distance/rate of speed
{{{6/(12-c)+6/(12+c)=16/15}}}
LCD:(12-c)(12+c)(15)
6(12+c)(15)+6(12-c)(15)=16(12+c)(12-c)
1080+90c+1080-90c=16(144-c^2)
2160=2304-16c^2
16c^2=144
c^2=9
c=±√9
c=±3
c=-3(reject, c>0)
or
c=3
rate of current=3 mph