Algebra/time problem

Question

Working at constant rates, Mary and John can complete a particular jigsaw puzzle in (x+1) hours and (x-1) hours respectively.
If they work together, the same jigsaw puzzle can be completed in (2/5)y minutes.
a) Express y in terms of x.
b) Hence, find the time taken by both of them to complete the jigsaw puzzle together if x=3. Give your answer in hours and minutes.

I've done problems similar to this before, but I just can't remember how to find the time taken for both of them to complete it together.

Answer 1

MARY:  Think of (x +1) hours to complete the puzzle as 1/(x +1) fraction of a puzzle completed in 1 hour.

JOHN:  Same thing:  1/(x -1) of a puzzle in 1 hour.

 

Together, adding the 2 fractions by finding a common denominator, we get 2x/(x² -1) of a puzzle per hour. Now flip it back again, and we get (x² - 1)/2x hours to complete it together.

So 60(x² - 1)/2x = (2/5)y minutes. Multiply by 5/2:

a) So y= 75(x² - 1)/x

 

b)     time to complete if x =3 is:  (3² - 1)/2(3) =  4/3 hrs or 80 min