Question

Б) Рабочий изготовил 10 деталей на своём станке за 52ч 30 мин; станок-автомат изготовил 25 таких же деталей за 43ч 45 мин. Во сколько раз автомат работал быстрее рабочего?

Answer 1

52 час 30 мин=52,5 час  (30:60=1/2=0,5)
43 час 45 мин=43,75 час (45:60=3/4=0,75)
52,5 час:10=5,25 час (тратит рабочий на 1 деталь)
43,75 час:25=1,75 час (тратит автомат на 1 деталь)
5,25 час:1,75 час=3 (раза)
Ответ: станок-автомат работает в 3 раза быстрее рабочего

Answer 2

Calculation of Time Taken by the Worker and the Machine

To determine how much faster the machine worked compared to the worker, we need to calculate the time taken by both the worker and the machine to produce the same number of parts.

The worker produced 10 parts in 52 hours and 30 minutes, which can be converted to 52.5 hours.

The machine, on the other hand, produced 25 parts in 43 hours and 45 minutes, which can be converted to 43.75 hours.

Calculation of the Ratio

To find out how many times faster the machine worked compared to the worker, we can calculate the ratio of the time taken by the worker to the time taken by the machine.

The ratio can be calculated as follows:

Ratio = Time taken by the worker / Time taken by the machine

Ratio = 52.5 hours / 43.75 hours

Calculating the ratio:

Ratio = 1.2

Conclusion

The machine worked approximately 1.2 times faster than the worker.