Question

A boat moves along the river flow from point A to B and returns back with the same speed. Speed of boat is $N$ times the speed of water. If the speed of water is $1m/s$, then the average speed of the boat (in m/s) is

• A.
  $\frac{N^2+1}{N}$
• B. $\frac{N^2-1}{N}$
• C.
  
  $N^2$
• D. $\frac{N^2+2}{N}$
  

Answer 1

The correct option is B $\frac{N^2-1}{N}$

When, boat moves from A to B it covers AB distance in time $t_{1}sec.$
given, Speed of the boat in flow = $N+1m/s$
As we know, $Speed=\frac{Distance}{Time}$
Then, $N+1=\frac{AB}{t_1}$
Similarly from B to A distance,
Speed of boat = $N-1m/s$
Let $t_{2}sec$be the time taken. Then, $N-1=\frac{BA}{t_2}$
Average speed =$\frac{2BA}{t_1+t_2}$ $m/s$
Substituting the values on above equation,
Average velocity = $\frac{N^2-1}{N}m/s$