Question

The speed of a boat in still water is $11$ km/hr and the speed of the stream is $x$ km/hr. Find in terms of $x$, the speed of boat upstream and the speed of boat downstream.
If the boat takes $2\frac{3}{4}$ hours to go 12 km upstream and then return, find the value of $x$.

• A. $1$
• B. $5$
• C. $9$
• D. $13$

Answer 1

The correct option is B $5$

Speed of the boat upstream $=(11-x)$ Km/hr
Speed of the boat downstream $=(11+x)$ Km/hr
Boat takes $\frac{11}{4}$ hours to go upstream and downstream.

Thus, $\frac{12}{11-x}+\frac{12}{11+x}=\frac{11}{4}$

$4(132+12x+132-12x)=11(121-x^2)$

$1056=1331-11x^2$
$11x^2=275$
$x^2=25$
$x=\pm 5$

Speed cannot be negative.
Thus, Speed of the stream is $5km/hr$