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 400400 hours and one that requires 500500 hours. if the teams work together, how long will it take to clean all of the streets? is this enough time before the cameras begin rolling?
Both crews will take 222.2 hours to complete the job.
No. The job won't be done before the cameras start rolling.
The crew that will take 400 hours does 1/400th of the total work required per hour.
The crew that will take 500 hours does 1/500th of the total work required per hour.
So if both crews work together, every hour will do 1/400 + 1/500.
Let's assume X is the number of hours. So let's make an equation and solve for X.
X/400 + X/500 = 1
500X/400 + 500X/500 = 500
500X/400 + X = 500
400*500X/400 + 400X = 400*500
500X + 400X = 200000
900X = 200000
X = 222.2222222
So both crews will take 222.222... hours to complete the job.
Now there's 7 days in a week and each day has 24 hours, so there's 7*24 = 168 hours in a week. And unfortunately, for the Mayor, that isn't enough time for both crews to be able to clean the streets.
