Question

Две машинистки, работая непрерывно и одновременно, перепечатали рукопись за 4 часа. Первая машинистка может сделать третью часть работы, выполненной второй машинисткой, на 100 минут быстрее, чем вторая машинистка сделает половину работы, выполненной первой машинисткой. Во сколько раз быстрее второй перепечатает всю рукопись первая машинистка, если они будут работать по отдельности?

Answer 1

X + Y = 4

1\3X + 5\3= 0.5Y 

X = 4-Y

1\3*(4-Y) + 5\3 = 1\2Y

4\3 - 1\3Y + 5\3 = 1\2Y

3 = 1\2Y + 1\3Y

18\6 = 3Y\6 + 2Y\6

5Y = 18

Y = 3.6 (часа) - вторая

X = 4-3.6 = 0.4 (часа) - первая

3.6 : 0.4 = 9 

ОТВЕТ: в 9 раз

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Problem Analysis

We have two typists working simultaneously to retype a manuscript. The first typist can complete one-third of the work done by the second typist 100 minutes faster than the second typist can complete half of the work done by the first typist. We need to determine how much faster the second typist can retype the entire manuscript compared to the first typist if they work separately.

Solution

Let's assume that the total time taken by the second typist to retype the entire manuscript is x hours. Therefore, the total time taken by the first typist to retype the entire manuscript will be x + 100 minutes.

Now, let's calculate the time taken by each typist to complete their respective portions of the work.

The first typist can complete one-third of the work done by the second typist 100 minutes faster than the second typist can complete half of the work done by the first typist.

Let's denote the time taken by the second typist to complete the entire work as t hours. Therefore, the time taken by the first typist to complete one-third of the work done by the second typist will be t - 100 minutes.

Now, let's set up an equation based on the given information:

t - 100 = (1/2)(x + 100)

Simplifying the equation:

2(t - 100) = x + 100

2t - 200 = x + 100

2t = x + 300

Now, let's calculate the time taken by each typist to complete the entire manuscript.

The first typist takes x + 100 minutes, which is equal to (x + 100)/60 hours.

The second typist takes x hours.

Since the first typist is completing the work in (x + 100)/60 hours and the second typist is completing the work in x hours, we can calculate the ratio of their speeds:

Speed ratio = (x + 100)/60 : x

To find how much faster the second typist is, we need to calculate the reciprocal of the speed ratio:

Faster ratio = x : (x + 100)/60

Simplifying the equation:

Faster ratio = 60x : x + 100

Now, let's calculate the value of the faster ratio:

Faster ratio = 60x / (x + 100)

To find the value of the faster ratio, we need to solve the equation:

2t = x + 300

Let's solve the equation to find the value of x:

2t - 300 = x

Now, substitute the value of x in the faster ratio equation:

Faster ratio = 60(2t - 300) / (2t - 300 + 100)

Simplifying the equation:

Faster ratio = 120t - 18000 / 2t - 200

Therefore, the second typist can retype the entire manuscript 120t - 18000 / 2t - 200 times faster than the first typist.

Answer

The second typist can retype the entire manuscript 120t - 18000 / 2t - 200 times faster than the first typist, where t is the time taken by the second typist to retype the entire manuscript.