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?

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reinhard10158 reinhard10158 · Answer 1 · 2022-02-01T22:34:23+01:00

Step-by-step 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.