SOLUTION: Gardener A can mow an entire lawn in 1 hour less than gardener B .If they work together they can mow the lawn in 20/9 hours how many hours will it take gardener A to mow the lawn a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Gardener A can mow an entire lawn in 1 hour less than gardener B .If they work together they can mow the lawn in 20/9 hours how many hours will it take gardener A to mow the lawn a      Log On


   

Question 626926: Gardener A can mow an entire lawn in 1 hour less than gardener B .If they work together they can mow the lawn in 20/9 hours how many hours will it take gardener A to mow the lawn alone?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that A can mow the lawn in t hours.
Then, B can mow the lawn in t%2B1 hours.

In 1 hour, A can mow 1%2Ft fraction of the lawn.
In 1 hour, B can mow 1%2F%28t%2B1%29 fraction of the lawn.

Therefore, in 1 hour, A and B can together mow 1%2Ft+%2B+1%2F%28t%2B1%29=%282%2At%2B1%29%2F%28t%2A%28t%2B1%29%29 fraction of the lawn.

Thus, A and B can together mow the entire lawn in t%2A%28t%2B1%29%2F%282%2At%2B1%29 hours.

Given, t%2A%28t%2B1%29%2F%282%2At%2B1%29=20%2F9
9%2At%2A%28t%2B1%29=20%2A%282%2At%2B1%29
9%2At%5E2%2B9t=40%2At%2B20
9%2At%5E2-31%2At-20=0
9%2At%5E2-36%2At%2B5%2At-20=0
9%2At%2A%28t-4%29%2B5%2A%28t-4%29=0
%28t-4%29%2A%289%2At%2B5%29=0

Product of two quantities is zero if at least one of them is zero.
Therefore, either t-4=0 or 9%2At%2B5=0.

Since t is time and can't be negative so t-4=0 or t=4 is the solution.
Ans: Gardener A can mow the lawn alone in 4 hours.