A motor-boat travels downstream and then the same distance upstream in a river running at

MATHEMATICS · Multi-part · AoPS · Mathematics · One-Variable Linear Equations · One-Variable Linear Equations

Problem

A motor-boat travels

30\,\text{km}

downstream and then the same distance upstream in a river running at

3\,\text{km h}^{-1}

. The upstream journey takes

1

hour more than the downstream journey. (i) If the speed of the boat in still water is

v\,\text{km h}^{-1}

, obtain an equation in

v

that models the situation. (ii) Solve the equation to find the two possible values of

v

. (iii) Keeping in mind the physical conditions of the motion, select the acceptable value of

v

and state the speed of the boat in still water.