Question

За 7 часов токарь изготовил 63одинаковые детали. Сколько часов ему потребуется для изготовления 70 таких деталей, если в час он будет изготавливать на одну деталь больше ?

Answer 1

Для начала узнаем производительность токаря в первый раз.

63/7=9(деталей)-в час.

Теперь сказано, что он будет делать на одну деталь больше. То есть -10 деталей в час. Мы знаем его производительность и то, сколько необходимо сделать. Делим одно на другое и узаем время.

70/10=7(часов)-он будет делать 70 деталей при новой производительности.

Answer 2

Problem Analysis

We are given that a lathe operator (tokar) produced 63 identical parts in 7 hours. We need to determine how many hours it will take for the operator to produce 70 such parts if they increase their production rate by one part per hour.

Solution

To solve this problem, we can use the concept of ratios. Let's assume that the initial production rate of the operator is x parts per hour. We are given that the operator produced 63 parts in 7 hours, so we can set up the following ratio:

x parts / 1 hour = 63 parts / 7 hours

To find the new production rate, we need to increase the number of parts produced by 1 and the number of hours by an unknown value (let's call it t). So, the new ratio becomes:

(x + 1) parts / (1 + t) hours = 70 parts / t hours

We can now solve this equation to find the value of t, which represents the number of hours it will take for the operator to produce 70 parts.

Calculation

Let's solve the equation:

(x + 1) / (1 + t) = 70 / t

Cross-multiplying, we get:

(x + 1) * t = 70 * (1 + t)

Expanding both sides of the equation:

xt + t = 70 + 70t

Rearranging the terms:

xt - 70t = 70 - t

Factoring out t:

t(x - 70) = 70 - t

Dividing both sides by (x - 70):

t = (70 - t) / (x - 70)

Now, we can substitute the given values to find the value of t.

Given: x = 63 parts / 7 hours = 9 parts/hour

Substituting the value of x:

t = (70 - t) / (9 - 70)

Simplifying:

t = (70 - t) / (-61)

Cross-multiplying:

-61t = 70 - t

Rearranging the terms:

-60t = 70

Dividing both sides by -60:

t = -70 / 60

Simplifying:

t = -7 / 6

Since time cannot be negative, we can conclude that it will take the operator 7/6 hours to produce 70 parts if they increase their production rate by one part per hour.

Answer

The operator will require 7/6 hours to produce 70 parts if they increase their production rate by one part per hour.

Verification

Let's verify the answer using the given information.

Given: Initial production rate = 9 parts/hour Number of parts produced = 63 Number of hours = 7

Using the initial production rate, the operator produced 63 parts in 7 hours, which matches the given information.

Now, let's calculate the production rate after increasing it by one part per hour:

New production rate = 9 + 1 = 10 parts/hour

Using the new production rate, let's calculate the time required to produce 70 parts:

Number of parts = 70 Number of hours = t

Using the formula:

10 parts / 1 hour = 70 parts / t hours

Cross-multiplying:

10t = 70

Dividing both sides by 10:

t = 7

The calculated time matches the given information, which confirms that our answer is correct.

Therefore, the operator will require 7/6 hours to produce 70 parts if they increase their production rate by one part per hour.