1.5 #27 - Please help me solve this!!

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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?

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

let the speed of boat in still water be "x" and "t" be the time to go upstream

so speed while upstream, is  x -2 and
speed while downstream = x +2

and time t to go 18 miles upstream
and time (4-t) to go 21 mile downstream

distance in upstream  18 = (x-2) t
distance in downstream 21 = (x +2 )(4-t)

from 1st equation t = 18/ (x-2)
putting in 2nd equation

21 = (x +2 ) (4 -18/(x-2))
21 (x -2) = (x+2)4(x - 2) -18(x+2)
21x - 42 = 4(x^2 -4) - 18x - 36
21x - 42 = 4x^2 - 16 - 18x - 36
4x^2 -39x -10 = 0
4x^2 - 40x +x -10 =0
4x(x-10)+1(x-10) =0

(4x-1)(x-10)=0
so, x =10

hence the speed of boat is 10 miles per hour

Let me know incase you need any further help ! Thanks :)
Sep 18th, 2015

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