A car in a straight road does half the route with an average speed of v₁ and the other half with an average speed of v₂. Determine the average speed vm of the whole travel.

From two cities, A and B, separated by a distance ΔS, depart, at sunrise, a car from each city to another with constant speeds. At noon they meet at a point on the road, the car departed from city A reaches city B at 16 o'clock, and the car that departed from city B reaches the city at 21 o'clock. Determine at what time the sunrise.

Two trains depart simultaneously from stations P and Q. The one from P goes to Q and the one from Q goes to P on parallel lines. The first train arrives at its destination 25 minutes after having passed the second, and the second train arrives at P 49 minutes after the intersection. What is the ratio of the speed of the two trains, knowing that their speeds are constant?

A car with a length of 3 m travels at a speed of 36 km/h. Calculate the exposure time to shoot the automobile in a 1.5 cm length film, knowing that the image remains reasonably clear it should not move more than the distance d = 0.1 mm on the negative.

From two small towns, connected by a straight-line road 10 km long, run two carts, pulled each by a horse and walking at the speed of 5 km/h. At the moment of departure, a fly, which was on the forehead of the first horse, start to fly at a speed of 15 km/h and will land on the forehead of the second horse. After a negligible time depart again, with the same speed as before, toward the first horse, until landing on his forehead. It continues in this trip until the two horses meet and the fly dies crushed between the two foreheads. How many kilometers went through the fly?

Two bodies start their motion at the same time from two points located on straight lines that make an angle of 60°. The first body starts from a point located at 3 m from the vertex with a speed of 5 m/s. The second body starts from a point 6 m from the vertex with a speed of 2 m/s. Both with constant velocity, determine after how long will they be separated from each other for a distance of 50 m.

A train of 100 m in length runs parallel to a car with negligible dimensions. Their movements are in a straight line, in the same direction, and the speed of the car is twice the train speed, both constants. What is the distance traveled by car to overtake the train?

Two trains of 120 and 280 meters in length move in straight parallel lines with constant speeds. When the two trains move in the same direction they are required 20 seconds for the first train to overtake the second, when they move in opposing directions are required 10 seconds for one to pass the other. Determine the speeds of the trains.

Two cars run a straight road with constant speeds v₂>v₁, the two cars run with a time interval T and from points separated by a distance D over the road. Assuming that car 1 starts motion before car 2, determine after how long, after car 2 starts, they will meet, assuming they move:
a) In the opposite directions;
b) In the same direction, from the position of car 2 to car 1.

A fox, chased by a greyhound, has 63 front jumps on the dog. The greyhound gives 3 jumps while the fox gives 4 jumps, but 6 jumps from the greyhound are worth 10 jumps of the fox. How many jumps the greyhound should give to reach the fox?