Two ducks move along the circumference of a circular pond in the same direction and come alongside each other every $54$ minutes. If they moved at the same speeds in the opposite directions, they would meet every $9$ minutes. It is known that when the ducks moved along the circumference in opposite directions, the distance between them decreased from $54 \mathrm{to} 14$ feet every $48$seconds. What is the speed of the slower duck?

Dev and Nishit started simultaneously from opposite points X and Y on a straight road, at constant speeds. When Dev had covered $40\%$ of the distance from X to Y, Nishit was $4 \mathrm{km}$ away from Dev after having crossed Dev. When Nishit had covered half the way, Dev was $10 \mathrm{km}$ short of the midpoint. Find the time it took Dev to cover the distance from X to Y to the time it took Nishit to cover the same distance.

Two ships sail in a fog towards each other with the same speed. When they are $4 \mathrm{km}$ apart, the captains decelerate the engines for $4 \mathrm{minutes}$ with a deceleration rate of $0.1 \mathrm{m}/{\mathrm{s}}^2$, and then the ships continue sailing with the speeds attained. For what range of values of the initial speed will the ships avoid collision?

Two towns are at a distance of $240 \mathrm{km}$ from each other. A motorist takes $8 \mathrm{hours}$ to cover the distance if he travels at a speed of ${\mathrm{V}}_{0 }\mathrm{km}/\mathrm{h}$ from town A to an intermediate town C, and then continues on his way with an acceleration of $x \mathrm{km}/{\mathrm{hr}}^2$. He needs the same time to cover the whole distance if he travels from A to Cat ${\mathrm{V}}_0 \mathrm{km}/\mathrm{h}$ and from C to B at ${\mathrm{V}}_1 \mathrm{km}/\mathrm{h}$ or from A to C at ${\mathrm{V}}_0 \mathrm{km}/\mathrm{h}$ and from C to B at ${\mathrm{V}}_0 \mathrm{km}/\mathrm{h}$. Find $V_0$ if the acceleration $\text{'}x\text{'}$ is double $V_0$ in magnitude and $V_0\ne V_1$.

Jaideep travels from Alaska, which is on a highway, to Burgen, which is 16 km from the highway. The distance between Alaska and Burgen along a straight line is $34 \mathrm{km}$. At what point should Jaideep turn from the highway to reach Burgen in the shortest possible time, if his speed along the highway is $10 \mathrm{km}/\mathrm{h}$ and $6 \mathrm{km}/\mathrm{h}$ otherwise.