Question

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?

Answer 1

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.