what's the answer for all of this?

1). Rove needs 4 days to mow the lawn at the council park. Harris and John, working together, need 3 days to do the same job. How long will it take Rove, Harris and John to do this job if they work together at the given rates?

2). Joanne is 9 years old and Jenny is 18 years old. After how many years will the ratio of Joanne's age to Jenny's age be 2:3?

3).Jamie sits for a test containing 25 questions. He is awarded 3 marks for each correct answer and 2 marks are subtracted for each incorrect answer. If he obtains 50 marks in the test, how many questions did she answer correctly?

Please give the answer and the working out so that I'll know how to do it next time.

Relevance
• Pranil
Lv 7

1). Rove needs 4 days in 1 day work done = 1/4

Harris and John, working together, need 3 days in 1 day work done by both = 1/3

work does the work in x days so in 1 day work done = 1/x

1/x + 1/4 = 1/3

1/x = 1/3 – 1/4 = 1/12

x = 12 days required by john

2). Joanne is 9 years old and Jenny is 18 years old.

Let after x years ratio is 2/3

after x years Joanne = (x + 9) and Jeny (x + 18)

ratio (x + 9)/(x + 18) = 2/3

3(x + 9) = 2(x + 18)

3x + 27 = 2x + 36

x = 9 after 9 years

3).Let correct answer be x and then wrong answers = (25 – x)

correct marks = 3x and wrong marks = 2(25 – x) are dedected

3x – 2(25 – x) = 50

3x – 50 + 2x = 50

5x = 100

x = 20 correct and 5 wrong.

-----

1) Not sure on bout this one, sorry

2) After 9 more years, Joanne will be 18 and Jenny 27, which is a 2:3 ratio

3) You have equations

x+y=25

3x-2y=50

Multiply the first eq by 2 and get 2x+2y=50

3x-2y=50 +

2x+2y=50

You get 5x=100 so x=20 If x=20, then y has to be 5 to satisfy both equations.

So Jamie got 20 right and 5 wrong.

2-

now Joanne is 9 years old and Jenny is 18 years old then after x years they will be 9+x,18+x

therefore, (9+x)/(18+x)=2/3

27+3x=36+2x

x=9

therefore Joanne is 18 years old and Jenny is 27 years old

3-

i supposed he solved them all,

3(x)-2(25-x)=50

5x-50=50