Three cars started simultaneously from Ajmer to Benaras along the same highway. The second car travelled with a speed that was $10 \mathrm{km}/\mathrm{h}$ higher than the first car's speed and arrived at Benaras $1 \mathrm{hour}$ earlier than the first car. The third car arrived at Benaras $33.33 \mathrm{minutes}$ earlier than the first car, travelling half the time at the speed of the first car and the other half at the speed of the second car. Find the total distance covered by these three cars during their journey between Ajmer and Benaras

Three sprinters A, B, and C had to sprint from points P to Q and back again (starting in that order). The time interval between the starting times of the three sprinters A, B, and C was 5 seconds each. Thus, C started $10$ seconds after A, while B started $5$ seconds after A. The three sprinters passed a certain point R, which is somewhere between P and Q simultaneously. Having reached Q and reversed the direction, the third sprinter met the second one $9$ m short of Q and met the first sprinter $15$ m short of Q. find the speed of the first sprinter if the distance between PQ is equal to $55$ m.

A passenger train left town Alpha for town Beta. At the same time, a goods train left Beta for Alpha. The speed of each train is constant throughout the whole trip. Two hours after the trains met, they were $450$km apart. The passenger train arrived at the place of destination $16$hours after their meeting and the goods train, $25$hours after the meeting. How long did it take the passenger train to make the whole trip?

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?