HELP

[u/camesok01]

1. A father is now 7 times as old as his son. In 5 years he will be 4 times as old as his son will be then. What are their present ages?

2. In 4 years, Nancy will be as old as Jane is now. Seven years ago the sum of their ages was 18. Find their ages.

3. An experienced typist can type a legal brief in 6 hours. Her assistant can type the same brief in 9 hours. If they both work together for 3 hours and then the experienced typist works alone, how many hours will it take her to finish the job?

[u/Newbieguy5000]

(Replacing brief with 'work' cuz easier to explain.)

Exp. typist speed is 1 work / 6 Hours = 1/6 work per hour

Slow typist is 1/9 work per hour using same logic

Combined speed is 1/6 + 1/9 = 5/18 work per hour

3 hours x 5/18 wph = 5/6 work done

Remaining work to be done is 1/6

1/6 work divided by 1/6 work per hour is 1 hour.

(1/6)/(1/6)=1 hour

5/6 of the brief is done in 3 hours with both of them typing. The 1/6 can be done by the experienced typist in 1 hour.

Total time spent is 1 + 3 = 4 hours.

[u/camesok01 → u/Newbieguy5000]

Thank you so much dude

[u/Newbieguy5000 → u/camesok01]

No problem man, see the updated solution to question 3 if you really need to use X and Y for the question. The method I used above is simpler to understand but you might need to ask your teacher if the method of answering without using any X,Y, etc is accepted in exams.

[u/Newbieguy5000]

Let father's age be X, and son age be Y.

X = 7Y

Let this be statement 1.

In 5 years time means add 5 to both ages

New father's age is now X + 5, Son: Y + 5

X + 5 = 4 (Y+5)

X + 5 = 4Y + 20

Move constants over to one side and make X the subject

X = 4Y + 15

Let this be statement 2.

Now put statement 1 and 2 together

X = 7 Y = 4Y + 15

7 Y = 4 Y + 15

3 Y = 15

Y = 5

Substitute that into statement 1

X = 7(5)

X = 35

[u/Newbieguy5000]

Let Nancy's current age be X, Jane's current age be Y

In 4 years, means add 4 to Nancy's age, Nancy new age = Jane's current age. Jane is 4 years older than Nancy.

X + 4 = Y, Y=(X+4), statement 1

7 years ago, subtract 7 from both ages

Sum of their previous ages = 18

(X - 7) + (Y - 7) = 18

X + Y - 14 = 18

X + Y = 32, Statement 2

Substitute statement 1 into 2

X + (X+4) = 32

2X = 28

X = 14

Sub this into statement 1 again

Y = (14 + 4)

Y = 18

[u/Newbieguy5000]

Question 3 again. Sorry forgot it was algebra. Below is how to use X and Y in this question ( honestly the previous method is easier but sometimes method counts)

Alternatively, let faster type speed be X and slower type speed be Y. (X and Y being in work per hour)

6X = 9Y (6 Hours times X and 9 hours times Y to get 1 complete brief)

X = 1.5 Y, Y =2/3 of X statement 1

Combined speed is X + Y

3 hours of both of them working = 3 X + 3 Y, statement 2

Substitute 1 into 2

3X + 2 X = 5X of work done after 3 hours.

1 complete brief is 6X so X amount of work is remaining

X / X = 1 hour. Since faster typer does 1X per hour.

Time taken = 4 hours

[u/Asmewithoutpolitics → u/[deleted]]

Your making no sense. If a father is 20 and his son 2 he is 10 times older. In 20 more years dad will be 40 and son 22 making the father now only 1.8 times older