Arun Sharma Solutions for Exercise 3: Level of Difficulty

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.

An object $\left(1\right)$ begins moving at a time moment $\mathrm{t}=0$ and $4 \mathrm{s}$ after the beginning of the motion, attains the acceleration of $3 \mathrm{m}/{\mathrm{s}}^2$. Find the distance covered by the object $\left(2\right)$ if the initial velocity of the second object is the same as the final velocity of the first object and it slows down at a rate of $2.6 \mathrm{m}/{\mathrm{s}}^2$ for $7 \mathrm{s}$. What is the distance covered by the second object while it is decelerating?

A motorboat moves from point A to point B and back again, both points being located on the river bank. If the speed of the boat in still water is doubled, then the trip from A to B and back again would take $20\%$ of the time that the motorboat usually spends in the journey. How many times is the actual speed of the launch higher than the speed of the river flow? 

A watch loses$\frac{2}{3}\%$ time during the $1^{\mathrm{st}}$ week and gains $\frac{1}{3}\%$ time during the next week. If on a Sun- day noon, it showed the right time, what time will it show at noon on the Sunday after the next.

Clocks A, B and C strikes every hour. B slows down and takes $2$min longer than A per hour while C become faster and takes$2$ min less than A per hour. If they strike together at $12$ midnight, when will they strike together again

A boat went down the river for a distance of $20$ km. It then turned back and returned to its starting point, having travelled a total of $7$ hours. On its return trip, at a distance of $12$ km from the starting point, it encountered a log, which had passed the starting point at the moment at which the boat had started downstream. The downstream speed of the boat is 

Two boats go downstream from point X to point Y. The faster boat covers the distance from X to Y $1.5$ times as fast as the slower boat. It is known that for every hour the slower boat lags behind the faster boat by $8$ km. However, if they go upstream, then the faster boat covers the distance from Y to X in half the time as the slower boat. Find the speed of the faster boat in still water.