Question
A motorboat covers the distance between two ports on the river in $t_1 = 8hr$ and $t_2 = 12hr$ downstream and upstream respectively. What is the time required for the boat to cover this distance in still water?
✓
Answer
Let x be the distance between the two ports. Let u be the velocity of the flow of water and v be the velocity of the boat in still water.
$\therefore \text{v}+\text{u}=\frac{\text{x}}{\text{t}_1}$ $\text{v}-\text{u}=\frac{\text{x}}{\text{t}_2}$
$\therefore \text{x}\Big(\frac{1}{\text{t}_1}+\frac{1}{\text{t}_2}\Big)=2\text{v}$
$\text{t}=\frac{\text{x}}{\text{v}}=\frac{2\text{t}_1\text{t}_2}{\text{t}_1+\text{t}_2}$
$=\frac{2\times8\times12}{8+12}=9.6\text{hr}$
$\therefore \text{v}+\text{u}=\frac{\text{x}}{\text{t}_1}$ $\text{v}-\text{u}=\frac{\text{x}}{\text{t}_2}$
$\therefore \text{x}\Big(\frac{1}{\text{t}_1}+\frac{1}{\text{t}_2}\Big)=2\text{v}$
$\text{t}=\frac{\text{x}}{\text{v}}=\frac{2\text{t}_1\text{t}_2}{\text{t}_1+\text{t}_2}$
$=\frac{2\times8\times12}{8+12}=9.6\text{hr}$
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