Question

traveling at full speed on a river, it takes 4 hours for a motorboat to travel 18 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?

Answer 1

where did you get this question ?

Answer 2

assume it takes t hours to go upstream'.
let speed of motorboat in still water=x
speed of current =2
(x-2)t=18
\[t=\frac{ 18 }{ x-2 }\] ...(1)
(x+2)(4-t)=21
\[(x+2)\left( 4-\frac{ 18 }{ x-2 } \right)=21\]
\[(x+2)\left( \frac{ 4x-8-18 }{ x-2 } \right)=21\]
\[(x+2)(4x-26)=21x-42\]
\[4x^2-26x+8x-52-21x+42=0\]
4x^2-39x-10=0
solve for x