SOLUTION: Another event at super challenge day is the lawn mower derby. Team members try to mow a standard sized lawn as quickly as possible. Terri and Candace can mow the lawn in 18min. If

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Another event at super challenge day is the lawn mower derby. Team members try to mow a standard sized lawn as quickly as possible. Terri and Candace can mow the lawn in 18min. If       Log On


   

Question 1084206: Another event at super challenge day is the lawn mower derby. Team members try to mow a standard sized lawn as quickly as possible. Terri and Candace can mow the lawn in 18min. If it takes Candace 30min to mow a lawn alone, how long does it take Terri to mow the lawn alone?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
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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.

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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Since Terri and Candace can mow the lawn in 18 min, they mow 1%2F18 of the lawn area per minute working together.


Since Candace can mow the lawn in 30 min, he (or she ?) mows 1%2F30 of the lawn area per minute working alone.


Hence, Terri working alone can mow 1%2F18-1%2F30 = 5%2F90-3%2F90 = 2%2F90 = 1%2F45 of the lawn area per minute.


Thus it will take 45 minutes for Terri to complete the job working alone.


Solved. 4 (four) lines to get the solution with mental calculations, without solving equations.


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It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".