Please solve

Question

this one I am struggling with 

2. Each of the following refers to three quantities. Introduce variables to represent the first two of these quantities, and then represent the third quantity in terms of the variables used for the first two.

 

Sue’s age; Mary’s age; the sum of Sue’s and Mary’s ages
Sue’s age; Mary’s age the difference between their ages five years from now. (Sue is older than Mary)
Sue’s age; Mary’s age half of Sue’s age two years ago
The number of minutes it takes Alphonse to do the job; how much-what portion-of the job they can do in one minute if they work together.

Answer 1

Let S be Sue's age and M be Mary's age.

 

1) sum means add so S + M

2) 5 years from now means they are both 5 years older, so, S + 5 and M + 5 are their ages. The difference in their ages is then

   (S+5) - (M + 5). Since Sue was older, this is the positive difference.

3) Two years ago, Sue's age was S - 2 so half of it is 1/2( S - 2 )

4) your question is not complete but here's how work problems work in general.

 

If I can complete a job in 7 hrs, divide both by 7 and get that I can do 1/7 of a job in 1 hr.

If you can complete a job in 10 hrs. you can do 1/10 of a job in 1 hr.

If we work together, we can do 1/7 + 1/10  in 1 hr = 17/70 of the job in 1 hr.

 

If you now multiply by 70/17 you get the whole job is done in 70/17 hrs or 4 and 2/70 of an hr or 4hrs and 1.7 minutes.

 

Alphonse can do a job in A min. So 1/A of the job in 1 min.

But then you start talking about working together when nobody else is mentioned ????

So let's say Bob can do the job in B mins, or 1/B of the job in 1 min

 

working together then is 1/A + 1/B of the job in 1 minute.