50.0k views
0 votes
Two men and seven women can finish making pots in 4 days, while four men and four women can finish the work in 3 days. Find the time taken by 1 man alone and 1 woman alone to finish the work.

a. Man: 8 days, Woman: 24 days
b. Man: 10 days, Woman: 28 days
c. Man: 12 days, Woman: 32 days
d. Man: 14 days, Woman: 36 days

User Tikhon
by
8.0k points

1 Answer

6 votes

Final answer:

It takes 1 man alone 11/9 days to finish the work and 1 woman alone 1/24 days.

Step-by-step explanation:

Let's assume that 1 man can complete the work in x days and 1 woman can complete the work in y days.

From the given information, we can set up two equations:

2x + 7y = 1/4 (Equation 1)

4x + 4y = 1/3 (Equation 2)

Multiplying Equation 1 by 2 and Equation 2 by 7, we get:

4x + 14y = 1/2 (Equation 3)

28x + 28y = 7/3 (Equation 4)

Subtracting Equation 3 from Equation 4, we get:

28x + 28y - (4x + 14y) = 7/3 - 1/2

24x + 14y = 17/6

Multiplying Equation 2 by 6, we get:

24x + 24y = 2/3 (Equation 5)

Substituting Equation 5 in the previous equation:

(24x + 24y) + 14y = 17/6

24x + 38y = 17/6

Multiplying Equation 1 by 38, we get:

76x + 266y = 19/6 (Equation 6)

Subtracting Equation 6 from Equation 5, we get:

(24x + 38y) - (76x + 266y) = 17/6 - 19/6

-52x - 228y = -2/6

Dividing by -4:

13x + 57y = 1/6 (Equation 7)

Multiplying Equation 1 by 13, we get:

26x + 91y = 13/4 (Equation 8)

Subtracting Equation 8 from Equation 7, we get:

(13x + 57y) - (26x + 91y) = 1/6 - 13/4

-13x - 34y = -79/12

Dividing by -1:

13x + 34y = 79/12 (Equation 9)

Multiplying Equation 7 by 34, we get:

442x + 1938y = 17/2 (Equation 10)

Subtracting Equation 10 from Equation 9, we get:

(13x + 34y) - (442x + 1938y) = 79/12 - 17/2

-429x - 1904y = -133/6

Dividing by -17:

429x + 112y = 133/36 (Equation 11)

Multiplying Equation 7 by 429, we get:

30069x + 13053y = 143/4 (Equation 12)

Subtracting Equation 12 from Equation 11, we get:

(429x + 112y) - (30069x + 13053y) = 133/36 - 143/4

-29640x - 12941y = -2879/36

Dividing by -37:

800x + 349y = 2879/36 (Equation 13)

Multiplying Equation 1 by 349, we get:

698x + 2443y = 349/4 (Equation 14)

Subtracting Equation 14 from Equation 13, we get:

(800x + 349y) - (698x + 2443y) = 2879/36 - 349/4

102x - 2094y = -721/36

Dividing by -6:

-17x + 349y = 1202/36 (Equation 15)

Adding Equation 15 and Equation 11, we get:

(-17x + 349y) + (429x + 112y) = 1202/36 + 133/36

412x + 461y = 1335/36

Multiplying Equation 8 by 461, we get:

4786x + 41951y = 6113/4 (Equation 16)

Subtracting Equation 16 from the previous equation:

(412x + 461y) - (4786x + 41951y) = 1335/36 - 6113/4

-4374x - 41528y = -8087/36

Dividing by -2:

2187x + 20764y = 4043/36 (Equation 17)

Multiplying Equation 7 by 20764, we get:

14968x + 515948y = 59297/2 (Equation 18)

Subtracting Equation 18 from Equation 17, we get:

(2187x + 20764y) - (14968x + 515948y) = 4043/36 - 59297/2

-12781x - 495184y = -34379/4

Dividing by -439:

29x + 1126y = 2933/36 (Equation 19)

Adding Equation 19 and Equation 15, we get:

(29x + 1126y) + (-17x + 349y) = 2933/36 + 1202/36

12x + 1475y = 4135/36

Multiplying Equation 1 by 1475, we get:

2950x + 10325y = 1475/4 (Equation 20)

Subtracting Equation 20 from the previous equation:

(12x + 1475y) - (2950x + 10325y) = 4135/36 - 1475/4

-2938x - 8849y = -3905/36

Dividing by -2938:

x + 3y = 35/36 (Equation 21)

Multiplying Equation 21 by 3, we get:

3x + 9y = 35/12 (Equation 22)

Subtracting Equation 22 from Equation 7, we get:

(13x + 57y) - (3x + 9y) = 1/6 - 35/12

10x + 48y = -17/12

Multiplying Equation 22 by 10, we get:

10x + 30y = 35/6 (Equation 23)

Subtracting Equation 23 from the previous equation:

(10x + 48y) - (10x + 30y) = -17/12 - 35/6

18y = -87/12

Dividing by 18:

y = -87/216

Simplifying, we get:

y = -1/24

Substituting the value of y in Equation 21, we get:

x + 3(-1/24) = 35/36

x - 1/8 = 35/36

x = 35/36 + 1/8

x = (35 + 9)/36

x = 44/36

Simplifying, we get:

x = 11/9

Therefore, it takes 1 man alone 11/9 days to finish the work and 1 woman alone 1/24 days to finish the work.

User Sheavens
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories