|
Question 1158064: Cara and Jim, working together, can weed the garden in 2 hours. Working alone, Jim takes twice as long as Cara. How long does it take Cara to weed the garden alone?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
Let C be the rate of work by Cara, and let J be the rate of work of Jim.
Then from the condition, you have these two equations
C + J =  (1) (their combined rate of work is of the job per hour)
C = 2J (2) (Cara's rate is twice the Jim's rate)
Next. you substitute expression (2) into (1), and you get
2J + J = , or
3J = , J =  .
It means that Jim will complete the job alone in 6 hours.
It implies that Cara will complete the job in 3 hours, working alone.
Solved.
If this solution seems to be too complicated, there is another way, without using equation.
You may interpret the condition in this way:
Two instances of Jim (as Cara) and one real Jim can complete the job in 2 hours.
2 + 1 = 3.
Hence, Jim alone can do the job in 2*3 = 6 hours.
Cara takes only half of that time, i.e. 6:2 = 3 hours.
You get the same answer.
Solved.
----------------
It is a standard and typical joint work problem.
There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See introductory 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".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Cara works twice as fast as Jim.
So when working together, Cara does 2/3 of the job and Jim does 1/3.
Working together it takes the two of them 2 hours to do the job.
So in 2 hours Cara completes 2/3 of the job.
So it will take her 3 hours to complete the whole job alone.
|
|
|
| |
