Traveling at full speed on a river, it takes 4 hours for a motor boat to travel 18 miles upstream and 21 miles back downstream. If the current's speed is 2 mph, what is the maximum speed of the boat in still water?
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let the speed of boat in still water be "x" and "t" be the time to go upstreamso speed while upstream, is x -2 andspeed while downstream = x +2
and time t to go 18 miles upstreamand time (4-t) to go 21 mile downstreamdistance in upstream 18 = (x-2) tdistance in downstream 21 = (x +2 )(4-t)from 1st equation t = 18/ (x-2)putting in 2nd equation21 = (x +2 ) (4 -18/(x-2))21 (x -2) = (x+2)4(x - 2) -18(x+2)21x - 42 = 4(x^2 -4) - 18x - 3621x - 42 = 4x^2 - 16 - 18x - 364x^2 -39x -10 = 04x^2 - 40x +x -10 =04x(x-10)+1(x-10) =0(4x-1)(x-10)=0so, x =10 hence the speed of boat is 10 miles per hour
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