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Solving problems for oncoming traffic
Multiplication by numbers ending in zeros
In this lesson we will look at solving oncoming traffic problems. First, let's remember the concept of average speed, how speed, time and distance are related. Next, we will solve three problems for finding 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 "convergence speed".
You are already familiar with the concept of "average speed" and you know how the quantities speed, time and distance are related. We will solve more complex problems.
Two skiers went out to meet each other at the same time from two villages and met after 3 hours. The first skier walked at an average speed of 12 km / h, the second - 14 km / h. Find the distance between 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 has traveled. To find the distance traveled by a skier, you need to know his average speed and the time he was on the way.
We know that the skiers went out to meet each other at the same time and were on the way for 3 hours. This means that each skier was on the way for three hours.
Average speed of one skier is 12 km / h, travel time is 3 hours. If we multiply the speed by time, then we find out how far the first skier traveled:
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 traveled, 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 went 14 km towards the first skier. We can find the speed of convergence:
We know that for every hour, skiers approached each other by 26 km. Then we can find how far they approached in 3 hours.
By multiplying the approach speed by 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 left at the same time 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 traveled and the speed of both skiers.
We know that every hour the first skier approached the meeting point by 12 km, and the second skier approached the meeting point by 14 km. That is, together they approached each hour by:
We found the speed of the skiers' convergence.
We know all the distance skiers have traveled and we know the speed of approach. If the distance is divided by the speed, then we get the time after which the skiers met.
Answer: the skiers met in 3 hours.
From two villages, the distance between which is 78 km, two skiers went out to meet each other at the same time 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 way. To find out how far the second skier traveled to the meeting point, you need to know how far the first skier traveled and the total distance. We know the total distance covered by both skiers - 78 km. To find the distance traveled by the first skier, you need to know his average speed and the time he was on the way. The average speed of the first skier was 12 km / h; he traveled for three hours. If the speed is multiplied by the time, we get the distance that the first skier traveled.
We know the total distance, 78 km, and the distance traveled by the first skier, 36 km. We can find out how far the second skier went.
We now know what distance the second skier covered, and we know how long he was on the way - 3 hours. If the distance traveled by the second skier is divided by the time he was on the way, we get his average speed.
Answer: the average speed of the second skier is 14 km / h.
Today we have learned to solve problems of oncoming traffic.
Bibliography
- Mathematics. Textbook for 4 cl. early shk. At 2 pm / M.I. Moreau, M.A. Bantov. - M .: Education, 2010.
- Demidova T.E., Kozlova S.A., Tonkikh A.P. Mathematics. 4th grade. Textbook in 3 hours, 2nd ed., Rev. - M .: 2013 .; Part 1 - 96 s., Part 2 - 96 s., Part 3 - 96 s.
- Mathematics: textbook. for the 4th class. general education. institutions with rus. lang. learning. At 2 o'clock, Part 2 / T.M. Chebotarevskaya, V.L. Drozd, A.A. Joiner; per. from white lang. L.A. Bondareva. - 3rd ed., Rev. - Minsk: Nar. asvet, 2008 .-- 135 p .: ill.
- Uchit.rastu.ru ().
- For6cl.uznateshe.ru ().
- Volna.org ().
Homework
- Try to solve problem number 3 in a different way.
- The distance between the two cyclists is 240 m. They rode towards each other at the same time and met in 30 seconds. What is the speed of the first cyclist if the speed of the second is 3 m / s?
- Towards each other from two villages, the distance between which is 30 km, two pedestrians came out at the same time. One walked at a speed of 4 km / h, and the other at a speed of 5 km / h. How many kilometers will they approach each other in 1 hour? And in three hours?
Anonymous
Solution to the problem: 1. Find the speed of removal per hour for two skiers, if the speed of the first and second skiers is known. 15 + 10 = 25 kilometers. 2. Find out how many kilometers they will move from each other in 1 hour. 25 * 1 = 25 kilometers. 3. Let's calculate at what distance from each other they will be in 2 hours. 25 * 2 = 50 kilometers. 4. Determine the distance between the skiers 3 hours after the start of the 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 the uniform movement of the body:
- V = S / t;
- V is the speed of body movement;
- S - the path traversed by the body during the movement;
- t is the time spent by an object or body on the way.
An object can be either a person or any object (car, plane, cannonball) that moves. The size of the object itself is neglected.
We are given the speed indicators of each of the skiers and three time intervals to determine the relative position of the skiers relative to each other. The exit time is the same.
Determine the distance traveled
Skiers move in different directions. We find the distances traveled by each and add them to 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 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 will pass 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 will 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 coincided.
Answer: in an hour the distance between skiers will be 25 km, in two hours - 50 km, in three hours - 75 km.
