SOLUTION: twin brothers, andy and brian, can mow their grandparents lawn together in 30 minutes. brian can mow the lawn himself in 11 minutes more than it takes andy. how long does it take f

Algebra ->  Rate-of-work-word-problems -> SOLUTION: twin brothers, andy and brian, can mow their grandparents lawn together in 30 minutes. brian can mow the lawn himself in 11 minutes more than it takes andy. how long does it take f      Log On


   

Question 741429: twin brothers, andy and brian, can mow their grandparents lawn together in 30 minutes. brian can mow the lawn himself in 11 minutes more than it takes andy. how long does it take for them to mow the lawn alone?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The rate is as "mow the lawn" in number of minutes, jobs per minute.

Andy+Brian, rate is 1 job per 30 minutes, or 1/30 job/min.
Andy, rate is unknown 1/(w) job/min, where w is the time it takes Andy to do one job.
Brian, rate is 1/(11+w), because, "11 minutes more than it takes andy."

The rates of each brother are additive when they work together, and we have THAT value.
highlight%281%2Fw%2B1%2F%2811%2Bw%29=1%2F30%29
Remember, w is a quantity of minutes.

Multiplying both sides of the equation by 30w(11+w),
30%28w%2B11%29%2B3w=w%5E2%2B11w
30w%2B330%2B3w=w%5E2%2B11w
33w%2B330=w%5E2%2B11w
w%5E2-22w-330=0

Solution to Quadratic Formula: w=%2822%2Bsqrt%2822%5E2-4%2A%28-330%29%29%29%2F2
highlight%28w=32%29 minutes.

RESULT: Andy does the job in 32 minutes, and Brian does the job in 43 minutes.