Question

На изготовление 50 деталей мастер затрачивает 1 ч 40 мин, а его ученик работает в 2 раза медленнее. За сколько минут ученик делает одну деталь? Решите задачу двумя способами...

Answer 1

1 ч. 40 мин- это 60=40=100 мин.
100/50=2 мин. уходит у мастера на изготовление одной детали
(100/50)*2=4 мин. уходит у ученика на изготовление одной детали
2-ой способ
100/50=2
2*2=4 мин

Answer 2

Problem Statement

Мастер затрачивает 1 час 40 минут на изготовление 50 деталей. Его ученик работает в 2 раза медленнее. За сколько минут ученик сделает одну деталь? Решите задачу двумя способами.

Solution 1: Using Proportions

To solve this problem, we can set up a proportion to find the time it takes for the apprentice to make one part.

Let's denote the time taken by the master to make 50 parts as M minutes. We know that M = 100 minutes (1 hour 40 minutes).

Let's denote the time taken by the apprentice to make one part as A minutes.

According to the problem, the apprentice works at half the speed of the master. Therefore, the proportion can be set up as:

M : A = 50 : 1

Substituting the values, we get:

100 : A = 50 : 1

Cross-multiplying, we get:

100 * 1 = 50 * A

Simplifying, we find:

A = 100/50 = 2 minutes

Therefore, the apprentice takes 2 minutes to make one part.

Solution 2: Using Ratios

Another way to solve this problem is by using ratios.

Let's denote the time taken by the master to make 50 parts as M minutes. We know that M = 100 minutes (1 hour 40 minutes).

Let's denote the time taken by the apprentice to make one part as A minutes.

According to the problem, the apprentice works at half the speed of the master. Therefore, the ratio of the apprentice's time to the master's time is 1:2.

We can set up the following ratio:

A : M = 1 : 2

Substituting the values, we get:

A : 100 = 1 : 2

Cross-multiplying, we get:

A * 2 = 100 * 1

Simplifying, we find:

A = 100/2 = 50 minutes

Therefore, the apprentice takes 50 minutes to make one part.

Conclusion

In conclusion, the apprentice takes 2 minutes to make one part according to the first solution using proportions, and 50 minutes according to the second solution using ratios. Both solutions yield the same result, but the approach used differs.