SOLUTION: Helping my child do her math and could use some help. Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person A could mow the lawn b

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Helping my child do her math and could use some help. Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person A could mow the lawn b      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 863009: Helping my child do her math and could use some help.
Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person A could mow the lawn by himself in 13 minutes less time than person B. How long does it take each person to mow the lawn by himself.
Many thanks in advance,
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

The Set-Up concept is how much Lawn per minute:

    A  + B = together

 1%2F%28x-13+%29+%2B+1%2Fx+=+1%2F42  Multiplying thru by 42x(x-13) so as all denominators = 1

   42x + 42(x-13) = x(x-13)

   84x - 546 = x^2 - 13x

  x^2 -97x + 546 = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2897+%2B-+sqrt%28+7225+%29%29%2F%282%29+

x+=+%2897+%2B-+85%29%2F%282%29+

      x =  182/2 = 91min    |Note must be more than 42, root of 6 is Extraneous

B takes ++highlight_green%2891min%29+ 

and..

 1/78 + 1/91 = 1/42

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/B+1/(B-13)=1/42
A=B-13
B=91
A=78