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 700 hours and one that requires 600 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

Explanation:

1 week = 7 days of 24 hours each = 7×24 = 168 hours.

the first team can do 1/700 of the total work per hour.

the second team can do 1/600 if the total work per hour.

if they work together, then 1/700 + 1/600 of the total work can be done per hour.

to add these 2 fractions we need to bring them to the same denominator. and that would be 4200 (LCM of 700 and 600).

1/700 + 1/600 = 6/4200 + 7/4200 = 13/4200

so, together, they can do 13/4200 if the total job in 1 hour.

how many hours will they need together to finish the job ?

well, how often does 13 fit into 4200 (as 4200/4200 is the complete job) ?

4200 / 13 = 323.0769231... hours

so, it will still take a little bit over 323 hours to clean all the streets.

but there are only 168 hours until the film crew starts.

so, no, there is not enough time.