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« The tourist is walking from the same city» — 181 tasks found
(views: 1403 , answers: 91 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 9 kilometers. Determine how many kilometers the tourist walked on the fourth day, if he walked the entire route in 10 days, and the distance between the cities is 180 kilometers.
Answer: 15
Task B14 ()(views: 720 , answers: 57 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 12 kilometers. Determine how many kilometers the tourist walked on the fifth day, if he walked the entire route in 10 days, and the distance between the cities is 255 kilometers.
Answer: 24
Task B14 ()(views: 765 , answers: 33 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the fifth day, if he walked the entire route in 10 days, and the distance between the cities is 145 kilometers.
Answer: 14
Task B14 ()(views: 670 , answers: 20 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 12 kilometers. Determine how many kilometers the tourist walked on the fourth day, if he walked the entire route in 10 days, and the distance between the cities is 210 kilometers.
Answer: 18
Task B14 ()(views: 628 , answers: 16 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 75 kilometers.
Task B14 ()(views: 642 , answers: 14 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 11 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 81 kilometers.
The correct answer has not yet been determined
Task B14 ()(views: 600 , answers: 14 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 9 kilometers. Determine how many kilometers the tourist walked on the fourth day, if he walked the entire route in 7 days, and the distance between the cities is 84 kilometers.
The correct answer has not yet been determined
Task B14 ()(views: 805 , answers: 13 )
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 120 kilometers.
Arithmetic progression. The exam task types include progression tasks. This word problems. The tasks are extremely simple, in school course There are more complex examples in this topic. It is necessary to understand the very essence - what an arithmetic and geometric progression is, and also to know the formulas (they need to be learned). So, it is known that there are various sequences numbers, there are many of them, for example:
23. 6, 89, 3, -2, 4 ...
2,3; 8; 90: 45,5 ...
Numbers can be fractional, decimal, etc... So:
An arithmetic progression is a sequence of numbers in which each subsequent number differs from the previous one by the same amount. This quantity is called the difference of an arithmetic progression and is denoted by the letter d.
a n +1 =a n +d n = 1,2,3,4…(d is the difference)
Each subsequent term of an arithmetic progression equal to the sum previous and number d .
Examples of arithmetic progression:
2,5,8,11,14,17… a 1 = 2 a 2 = 5 d = 3
1,2,3,4,5,6,7,8… a 1 = 1 a 2 = 2 d = 1
Formula for the nth term:
Formula for the sum of the first n terms:
Substitute a n =a 1 +d (n – 1) into it, and we get another one:
There is another type of progression.
Each subsequent member geometric progression equal to the product previous and number q .
bn +1 = bn q n = 1, 2, 3... (q is the denominator of the geometric progression).
Examples of geometric progression:
2, 6, 18, 54, 162… b 1 = 2 b 2 = 5 q = 3
2, 4, 8, 16, 32, 64, 128… b 1 = 2 b 2 = 5 q = 2
Formula for the nth term:
Sum Formula n first terms q ≠ 1:
Substitute b n = b 1 q n –1 into it, and we get another one:
These are the formulas you need to know (very well). You will see that the tasks presented below are simple. It is necessary to immediately indicate the initial data: where is the sum, where is the first term, where is the number of the nth term or the number of the first terms.
Let's consider the tasks:
A tourist walks from one city to another, each day walking more than the previous day, over the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 120 kilometers.
A tourist walks every day more than the previous day by the same number of kilometers. This is an arithmetic progression problem. The number of days is the number of terms of the progression n = 6, 120 kilometers is the sum of the distances covered every day (the sum of all terms of the progression S), 10 kilometers is the first term of the progression, that is, a 1 = 10.
This means we can find d - the difference of the arithmetic progression. This is the number of kilometers by which the distance increases on each subsequent day:
That is, every day a tourist walks 4 kilometers more than the previous day. This means that on the second day the tourist will walk 10 + 4 = 14 kilometers, on the third day 14 + 4 = 18 kilometers. Or you can calculate using the formula for the nth term of the progression:
Answer: 18
The truck transports a load of crushed stone weighing 210 tons, increasing the transportation rate by the same number of tons every day. It is known that 2 tons of crushed stone were transported on the first day. Determine how many tons of crushed stone were transported on the ninth day if all the work was completed in 14 days.
The truck increases its freight rate by the same number every day. This is an arithmetic progression. The first term of the progression is equal to 2 (the number of tons transported on the first day). The progression amount is 210 ( total quantity transported crushed stone). The number of members of the progression is 14 (the number of days during which the cargo was transported). We use the formula for the sum of an arithmetic progression and find from it d - the number of tons by which the transportation rate increased every day:
Means,
Formula for the nth term of an arithmetic progression:
Thus, on the ninth day the truck transported:
Answer: 18
A snail crawls from one tree to another. Every day she crawls the same distance further than the previous day. It is known that for the first and last days a snail crawled in total 10 meters. Determine how many days the snail spent on the entire journey if the distance between the trees is 150 meters.
Every day the snail crawls the same distance further than the previous day. This is an arithmetic progression problem. The number of days is the number of members of the progression, 150 meters is the sum of all members of the progression), 10 meters is the sum of the distances on the first and last day (the sum of the first and last members of the progression). That is,
We use the formula for the sum of terms of an arithmetic progression:
Let's substitute:
The snail spent 30 days on the entire journey.
Answer: 30
Vera needs to sign 640 postcards. Every day she signs the same number of cards more than the previous day. It is known that Vera signed 10 postcards on the first day. Determine how many postcards were signed on the fourth day if all the work was completed in 16 days.
Vera signs the same number of postcards more than the previous day. This is an arithmetic progression problem. The number of days for which the work was completed is the number of members of the progression (n = 6), 640 postcards is the sum of all members of the progression (S = 640), 10 postcards is the first member of the progression, that is, a 1 = 10.
This means we can find d - the difference of the arithmetic progression. This is the number of postcards by which Vera increases her quota on each subsequent day:
Solution to prototypes of task B13 Andrey Gorbunov (graduate of 2013) 43 Prototype A tourist walks from one city to another, each day walking more than the previous day, the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 120 kilometers. 44 Prototype The truck transports a load of crushed stone weighing 210 tons, increasing the transportation rate by the same number of tons every day. It is known that 2 tons of crushed stone were transported on the first day. Determine how many tons of crushed stone were transported on the ninth day if all the work was completed in 14 days 45 Prototype A snail crawls from one tree to another. Every day she crawls the same distance further than the previous day. It is known that during the first and last days the snail crawled a total of 10 meters. Determine how many days the snail spent on the entire journey if the distance between the trees is 150 meters.
CONDITION Prototype of task B13 (99582) SOLUTION: The problem involves the use of the properties of arithmetic progression, but it can be solved as follows: Consider the distance traveled by day 1)10 The resulting equation is: 2)10+x 60+15x=120 3)10+2x 15x= 60 4)10+3x x=4 5)10+4x We are interested in the 3rd day: 6)10+5x 10+2*4=18 ANSWER:18 A tourist goes from one city to another, every day walking more than on the previous day, for the same distance. It is known that on the first day the tourist walked 10 kilometers. Determine how many kilometers the tourist walked on the third day, if he walked the entire route in 6 days, and the distance between the cities is 120 kilometers.
CONDITION Prototype task B13 (99583) ANSWER: 18 A truck transports a load of crushed stone weighing 210 tons, increasing the transportation rate by the same number of tons every day. It is known that 2 tons of crushed stone were transported on the first day. Determine how many tons of crushed stone were transported on the ninth day if all the work was completed in 14 days
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