Question

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours . It can travel 21 km upstream and return in 5 hours . Find the speed of the boat in still water and the speed of the upstream .

Answer 1

Let the speed of the boat in still water be x km/h and the speed of the stream be y km/h.
Speed of boat upstream = x − y
Speed of boat downstream = x + y
It is given that, the boat travels 30 km upstream and 28 km downstream in 7 hours.
$\therefore \frac{30}{x-y}+\frac{28}{x+y}=7$
Also, the boat travels 21 km upstream and return in 5 hours.
$\therefore \frac{21}{x-y}+\frac{21}{x+y}=5$
Let $\frac{1}{x-y}=u\mathrm{and}\frac{1}{x+y}=v$.
So, the equation becomes
$$\begin{gathered} 30u+28v=7.....\left(\mathrm{i}\right) \\ 21u+21v=5.....\left(\mathrm{ii}\right) \end{gathered}$$
Multiplying (i) by 21 and (ii) by 30, we get
$$\begin{gathered} 630u+588v=147...\left(\mathrm{iii}\right) \\ 630u+630v=150...\left(\mathrm{iv}\right) \end{gathered}$$
Solving (iii) and (iv), we get
$v=\frac{1}{14}$ and $u=\frac{1}{6}$
But, $\frac{1}{x-y}=u\mathrm{and}\frac{1}{x+y}=v$
So,
$$\begin{gathered} \frac{1}{x-y}=\frac{1}{6}\mathrm{and}\frac{1}{x+y}=\frac{1}{14} \\ \Rightarrow x-y=6\mathrm{and}x+y=14 \end{gathered}$$
Solving these two equations, we get
x = 10 and y = 4
So, the speed of boat in still water = 10 km/h and speed of stream = 4 km/h.