Question

Nakita recorded a video of homecoming highlights of the senior class and now everybody wants a copy. She promised to have 25 ready the next day but suddenly realized that it will take her ten hours to do that. Her friend, Abby, volunteered to help and she can do the job alone in 15 hours. How long will it take the girls, working together, to complete the job?

Answer 1

Answer: 6hours

Explanation:

it will take Nakita 10 hours to get 25 copies of the video ready

Then it takes Nakita 25/10 per hour to get 25 copies ready

it will take Abby 15 hours to get 25 copies of the video ready

Then it takes Abby 25/15 per hour to get 25 copies ready

It is assumed that they are working individually and simultaneously. This means their work rate is additive.

Their combined work rate per hour is

25/10 + 25/15 = 5/2 +5/3

=25/6 per hour

Let x hours be the time it will take them to get 25 videos ready.

It will take them 25/x per hour to get the videos ready

Equating both expressions,

25/x =25/6

25 × x = 25 × 6

x = 6 hours