SOLUTION: Billy and bobby can mow the lawn in 65 minutes together. Billy can mow the lawn alone in 30 minutes less than it would take bobby. How long would it take for bobby to mow the lawn

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Billy and bobby can mow the lawn in 65 minutes together. Billy can mow the lawn alone in 30 minutes less than it would take bobby. How long would it take for bobby to mow the lawn       Log On


   

Question 944677: Billy and bobby can mow the lawn in 65 minutes together. Billy can mow the lawn alone in 30 minutes less than it would take bobby. How long would it take for bobby to mow the lawn alone?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = time billy takes to mow the lawn alone.
Let B = time Bobby takes to mow the lawn alone.
The formula for the time it takes for them to work together is given by
(1) +T+=+1%2F%281%2Fb%2B1%2FB%29 which reduces to
(2) +T+=+%28b%2AB%29%2F%28b%2BB%29
We are given that
(3) T = 65 and
(4) b = B - 30
Substitute (3) and (4) into (2) and get
(5) 65+=+%28%28B-30%29%2AB%29%2F%28B-30%2BB%29 which simplifies to
(6)B%5E2+-160B%2B1950+=+0+
Use the quadratic equation to determine the two roots of (6) as
(7)+B+=+80+%2B-+sqrt%284450%29
Choose the positive square root because the negative square root makes b, which is 30 less than B, a negative time.
Therefore
(8) +B+=+80+%2B+sqrt%284450%29 or
B is approximately 146.708 minutes.
Then b 1s approximately 116.708 minutes.
Substituting these values into (2) gives
(9) T = (116.708*146.708)/(116.708+146.708) or
(10) T = 64.9998
Answer: Bobby takes about 146.7 minutes to mow the lawn alone.