Question 1084206
terri and candace can mow the lawn in 18 minutes when they work together.


candace takes 30 minutes when she mows the lawn by herself.


how long does it take terri to mow the lawn by herself?


rate * time = quantity


when they work together, they take 18 minutes to mow the lawn.


time = 18 minutes
quantity = 1 lawn



rate * time = quantity becomes rate * 18 = 1


solve for rate to get rate = 1/18 of the lawn in 1 minute.


when they work together, their combined rate to mow the lawn is 1/18 of the lawn in 1 minute.


when candace works alone, her rate is 1/30 of the lawn in 1 minute.


when they work together, their rates are additive.


you get 1/30 + x = 1/18


x is the rate that terri works at.
1/30 is the rate that candace works at.
1/18 is the rate that both working together work at.


solve for x to get x = 1/18 - 1/30


look for a common denominator.


looks like 90 will do it because 5 * 18 = 90 and 3 * 30 = 90


multiply 1/18 by 5/5 to get 5/90.


multiply 1/30 by 3/3 to get 3/90


x = 1/18 - 1/30 becomes x = 5/90 - 3/90 which becomes x = 2/90


you can simplify that to 1/45


terri works at the rate of 1/45 of the lawn in one minute.


rate * time = quantity becomes 1/45 * time = 1 for terri.


solve for time to get time = 45 minutes.


it takes candace 30 minuter working alone and it takes terri 45 minutes working alone.


the rate that candace works at is 1/30 of the lawn in one minute and the rate that terri works at is 1/45 of the lawn in one minute.


working together you get 1/30 * time + 1/45 * time = 1


factor out time and you get (1/30 + 1/45) * time = 1


take 90 as the common denominator of the fractions and you get (3/90 + 2/90) * time = 1 which becomes 5/90 * time = 1


solve for time to get time = 1 * 90 / 5 = 90/5 = 18 minutes


solution looks good.


solution is that it takes terri 45 minutes to mow the lawn alone.