Grades 9-10 Video Solutions 2014-Levels 9&10 Video Solutions 2014 problem13

Video Transcription

Question number 13. Six girls share an apartment with two bathrooms which they use every morning beginning at seven o'clock. They use the bathroom one at a  time and sit down to eat breakfast together as soon as the last girl is finished. They spend 9, 11, 13, 18, 22 and 23 minutes in the bathroom respectively.  If they are well organized, what is the earliest they can have breakfast together? So let's try to make a schedule here that is as efficient as  possible. We have bath one and bath two and then let's send the girls that take the longest first and note that the remaining times are 9, 11, 13 and 18 where  two of those pairs have the same difference and one pair has a larger difference of five. So we should separate those so that we have for example 18  over here and 13 over here and now we can tally up the time so far this is 40 minutes in bathroom one and here we have 36 minutes in bathroom two and we have  two remaining possibilities so we either have nine minutes added to bathroom one for a total of 49 or we have 11 minutes here for a total of 51 or we do the same  thing in bathroom two we had nine minutes here for a total of 45 and we can then add 11 minutes for a total of 47. So either way we see that with nine  here in bathroom one that's 49 minutes and 11 here in bathroom two that's 47 minutes like that the best time is 49 or with 11 in bathroom one we would have  to have nine in bathroom two and then the best time is 51 minutes because we have to wait until all the girls are finished. Likewise interchanging the 18  with the 13 would not produce a better time so overall waiting for all the girls to be done we see that in bathroom one we would have to have 22, 18 and 9 so  that's the result 22, 18 and 9 for a total of 49 minutes while 23, 13 and 11 produces 47 minutes but we only have a two-minute difference here between the  finish times so the earliest all girls are finished is at 7.49, 49 minutes after they begin using the bathroom and that's when they can eat breakfast together the answer here is B.

Video Summary

Six girls share two bathrooms and aim to finish their morning routine efficiently. With shower times of 9, 11, 13, 18, 22, and 23 minutes, the goal is to minimize total usage time. By strategically assigning longer shower times to the same bathroom and balancing the remaining times, the optimal schedule results in a total time of 49 minutes for bathroom one (with 22, 18, and 9-minute showers) and 47 minutes for bathroom two (with 23, 13, and 11-minute showers). Consequently, they can all have breakfast together at 7:49 AM, 49 minutes after starting.

Keywords

efficient morning routine

shower time optimization

bathroom schedule

time management

shared bathrooms