Speed. Two skiers left the same point at the same time in opposite directions. Speed ​​Let's determine the distances traveled

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Solution to the problem: 1. Find the speed of removal per hour of two skiers, if the speed of the first and second skier is known. 15 + 10 = 25 kilometers. 2. Find out how many kilometers they will move away from each other in 1 hour. 25 * 1 = 25 kilometers. 3. Let’s calculate how far apart they will be after 2 hours. 25 * 2 = 50 kilometers. 4. Determine the distance between skiers 3 hours after the start of movement. 25 * 3 = 75 kilometers. Answer: In an hour the distance between skiers will be 25 kilometers, in 2 hours 50 kilometers and in 3 hours 75 kilometers.

Anonymous

The solution of the problem

Let us recall the formula for uniform motion of a body:

• V = S/t;
• V is the speed of body movement;
• S is the distance traveled by the body during movement;
• t is the time an object or body is in transit.

The object can be either a person or any object (car, plane, cannonball) that moves. The dimensions of the object itself are neglected.

We are given speed indicators for each skier and three time intervals to determine the relative position of the skiers relative to each other. The release time is the same.

Let's determine the distances traveled

The skiers move away in different directions. We find the distances covered by each and adding them we get the required distance between them.

In one hour, the 1st skier will pass:

S = V *t = 15 km/h * 1 hour = 15 km.

The second skier will pass in an hour:

S = V * t = 10 km/h * 1 hour = 10 km.

The distance between them in an hour will be 15 km + 10 km = 25 km.

In two hours the 1st skier will pass:

S = V * t = 15 km/h * 2 hours = 30 km.

The second one will pass in 2 hours:

S = v * t = 10 km * 2 hours = 20 km.

In two hours there will be 30 km + 20 km = 50 km between them.

In three hours, the 1st skier will pass:

S = V * t = 15 km/h * 3 hours = 45 km.

The second one will take place in three hours:

S = 10 km/h * 3 hours = 30 km.

In three hours there will be 45 km + 30 km = 75 km between them.

Examination

Knowing the distance and time, we find the speed of each skier:

V 1 = 45 km / 3 h = 15 km / h;

V 2 = 30 km / 3 h = 10 km / h.

The speeds matched.

Answer: in an hour the distance between skiers will be 25 km, in two hours - 50 km, in three hours - 75 km.

Solving oncoming traffic problems
Multiplying by numbers ending in zeros

In this lesson we will look at solving problems involving oncoming traffic. First, let's remember the concept of average speed, how speed, time and distance are related. Next, we will solve three problems to find each of the quantities, according to the conditions of which the objects will move towards each other. Let's get acquainted with the concept of “approach speed”.

You are already familiar with the concept of “average speed” and know how the quantities speed, time and distance are related. Let's solve more complex problems.

Two skiers set out simultaneously towards each other from two villages and met 3 hours later. The first skier walked at an average speed of 12 km/h, the second - 14 km/h. Find the distance between the villages. See illustration in Figure 1.

Rice. 1. Illustration for problem 1

To find the distance between villages, we need to know how far each skier covered. To find the distance traveled by a skier, you need to know his average speed and the time he was on the road.

We know that the skiers set out towards each other at the same time and were on the road for 3 hours. This means that each skier was on the road for three hours.

The average speed of one skier is 12 km/h, travel time is 3 hours. If we multiply the speed by the time, we find out how far the first skier covered:

The average speed of the second skier is 14 km/h, the travel time is the same as that of the first skier - three hours. To find out how far the second skier has covered, multiply his average speed by his travel time:

Now we can find the distance between the villages.

Answer: the distance between the villages is 78 km.

In the first hour, one skier covered 12 km; in the same hour, the second skier covered 14 km towards the first skier. We can find the speed of approach:

We know that for every hour the skiers moved 26 km closer to each other. Then we can find how far they approached in 3 hours.

By multiplying the speed of approach by the time, we found out how far the two skiers traveled, that is, we found out the distance between the villages.

Answer: the distance between the villages is 78 km.

From two villages, the distance between which is 78 km, two skiers came out simultaneously towards each other. The first skier walked at an average speed of 12 km/h, and the second - 14 km/h. How many hours later did they meet? (See Figure 2).

Rice. 2. Illustration for problem 2

To find the time after which the skiers will meet, you need to know the distance that the skiers have covered and the speed of both skiers.

We know that every hour the first skier approached the meeting point at 12 km, and the second skier approached the meeting point at 14 km. That is, together they approached each hour by:

We found the speed of approach of the skiers.

We know the entire distance the skiers have covered and we know the closing speed. If we divide the distance by the speed, we get the time after which the skiers met.

Answer: the skiers met after 3 hours.

From two villages, the distance between which is 78 km, two skiers left simultaneously towards each other and met after 3 hours. The first skier walked at an average speed of 12 km/h. What was the average speed of the second skier? (See Figure 3.)

Rice. 3. Illustration for problem 3

To find out the average speed of the second skier, you need to find out how far the skier traveled to the meeting point and how long he was on the road. To find out how far the second skier has traveled to the meeting point, you need to know how far the first skier has traveled and the total distance. We know the total distance covered by both skiers - 78 km. To find the distance covered by the first skier, you need to know his average speed and the time he was on the road. The average speed of the first skier was 12 km/h; he was on the road for three hours. If we multiply the speed by the time, we get the distance covered by the first skier.

We know the total distance, 78 km, and the distance covered by the first skier, 36 km. We can find how far the second skier has covered.

We now know how far the second skier traveled, and we know how long he was on the road - 3 hours. If the distance covered by the second skier is divided by the time he was on the road, we get his average speed.

Answer: the average speed of the second skier is 14 km/h.

Today we learned to solve problems involving oncoming traffic.

Bibliography

1. Mathematics. Textbook for 4th grade. beginning school At 2 o'clock/M.I. Moreau, M.A. Bantova. - M.: Education, 2010.
2. Demidova T.E., Kozlova S.A., Tonkikh A.P. Mathematics. 4th grade. Textbook in 3 parts. 2nd ed., revised. - M.: 2013.; Part 1 - 96 p., Part 2 - 96 p., Part 3 - 96 p.
3. Mathematics: textbook. for 4th grade. general education institutions with Russian language training. At 2 p.m. Part 2 / T.M. Chebotarevskaya, V.L. Drozd, A.A. Carpenter; lane with white language L.A. Bondareva. - 3rd ed., revised. - Minsk: Nar. Asveta, 2008. - 135 pp.: ill.

1. Uchit.rastu.ru ().
2. For6cl.uznateshe.ru ().
3. Volna.org ().

Homework

1. Try solving problem #3 in a different way.
2. The distance between two cyclists is 240 m. They rode out simultaneously towards each other and met after 30 seconds. What is the speed of the first cyclist if the speed of the second is 3 m/s?
3. Two pedestrians came out at the same time from two villages, the distance between which is 30 km, towards each other. One was walking at a speed of 4 km/h, and the other was walking at a speed of 5 km/h. How many kilometers will they get closer to each other in 1 hour? And in three hours?