SOLUTION: A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before filming begins. Two teams are​ available, one tha

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before filming begins. Two teams are​ available, one tha      Log On


   

Question 1117873: A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before filming begins. Two teams are​ available, one that requires 200 hours and one that requires 300 hours. If the teams work​ together, how long will it take to clean all of the​ streets?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
One team makes  1%2F200 of the job per hour.


Another team makes  1%2F300  of the job per hour.


Working together, the teams make  1%2F200+%2B+1%2F300 = 3%2F600%2B2%2F600 = 5%2F600 = 1%2F120 of the job per hour.


Hence, the two teams will make the job in 120 hours working together.

Solved and explained.

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It is a typical and standard 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".


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(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You have two good solutions from other tutors using the traditional algebraic approach to this kind of problem.

Here is an alternative method for solving this kind of problem that many students find easier.

One crew takes 200 hours to do the job; the other takes 300 hours.

Consider the least common multiple of the two times; in this problem, 600 hours.

In 600 hours the first crew could complete 3 of these jobs; in 600 hours the second crew could complete 2 of them.

So together in 600 hours the two crews together could complete 5 of the jobs.

Then, to complete just the one job, the two crews would need to work for 600/5 = 120 hours.