Question

The boat sails down the river for $10$ km and then up the river for $6$ km. The speed of the river, flow is $1$ km/h. What is the minimum speedof the boat for the trip to take a maximum of 4hrs?

Answer 1

Let us assume the speed of the boat $x$ km/hr.

Speed of the boat in the direction of river flow $=(x+1)$ km/hr

Speed of the boat in the opposite direction of river flow $=(x-1)$ km/hr

Total time taken for trip $\Rightarrow \frac{10}{x+1}+\frac{6}{x-1}=4$

$\frac{10(x-1)+6(x+1)}{(x+1)(x-1)}=4\Rightarrow \frac{10x-10+6x+6}{x^2-1}=4\Rightarrow \frac{16x-4}{x^2-1}=4$

On solving we get $x=4$ km/hr.