Question

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boating till water.

• A. Speed of boat = 8 km/h & Speed of stream $=3$ km/hr
• B. Speed of boat = 8 km/h & Speed of stream $=4$ km/hr
• C. Speed of boat = 7 km/h & Speed of stream $=2$ km/hr
• D. Data insufficient

Answer 1

The correct option is A Speed of boat = 8 km/h & Speed of stream $=3$ km/hr

Let the speed of boat in still water$=x$ km\hr and The speed of stream$=y$ km\hr

Speed of boat at downstream

$\Rightarrow (x+y)km/hr$

Speed of boat at upstream

$\Rightarrow (x-y)km/hr$

$\because time=\frac{distance}{speed}$

Time taken to cover 30 km upstream $\Rightarrow \frac{30}{x-y}$

Time taken to cover 44 km downstream$\Rightarrow \frac{44}{x+y}$

According to the first condition,

$\Rightarrow \frac{30}{x-y}=\frac{44}{x+y}=10$

Time taken to cover 40 km upstream $\Rightarrow \frac{40}{x-y}$

Time taken to cover 55 km downstream $\Rightarrow \frac{55}{x+y}$

According to the second condition,

$\Rightarrow \frac{40}{x-y}=\frac{55}{x+y}=13$

Let $\frac{1}{x-y}=uand\frac{1}{x+y}=v$

$\Rightarrow 30u+44v=\mathrm{10.....}eq1$

$\Rightarrow 40u+55v=\mathrm{13.....}eq2$

Multiplying eq1 by 3 and eq2 by 5 and subtract both

$\Rightarrow (150u+220v=50)-(160u+220v=52)$

$\Rightarrow -10u=-2\Rightarrow u=\frac{1}{5}$

put $u=\frac{1}{5}$ in eq1

$\Rightarrow 30\times \frac{1}{5}+44v=10\Rightarrow 44v=4\Rightarrow v=\frac{1}{4}$

$\Rightarrow u=\frac{1}{x-y}=\frac{1}{5}\Rightarrow x-y=\mathrm{5...}eq3$

$\Rightarrow v=\frac{1}{x+y}=\frac{1}{11}\Rightarrow x+y=\mathrm{11...}eq4$

Subtracting eq3 and eq4, we get

$\Rightarrow x=8$

Put $x=8$ in eq3

$\Rightarrow y=3$

Hence, the speed of the boat in still water$=8$km\hr

The speed of stream$=3$km\hr