Question 887905
a speed boat takes 3 hours longer to go 45 miles up a river than to return. if the boat cruises at 20 mph in still water, what is the rate of the current
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let c=rate of current
20+c=speed of boat down river
20-c=speed of boat up river
travel time=distance/speed
{{{45/(20-c)-45/(20+c)=3}}}
lcd: (20+c)(20-c)
{{{45(20+c)-45(20-c)=3 (20+c)(20-c)}}}
900+45c-900+45c=3(20^2-c^2)=3(400-c^2)=1200-3c^2
90c=1200-3c^2
3c^2+90c-1200=0
c^2+30c-400=0
(c+40)(c-10)=0
c=-40 reject
or
c=10
rate of the current=10 mph