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?

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 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

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up