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Boxing Quincy

challenging math question!!! ?

Quincy and Celine have to move 16 small boxes and 10 large boxes. quincy takes 3 mins for the small box, and 5 mins for the big one. and celine takes 2 mins for the small box, and 6 mins for the big one. they start moving the boxes at 9:00 a,m. the earliest time at which they can be finished moving all of the boxes is
A) 9;41 a.m B) 9.42 a.m C) 9;43 a,m D) 9;44 a.m E) 9;45 a.m
I did this question myself, and I got the answer C. However. Most people found the answer by using try on error. Is anyone know how to solve this question by using other method? Such as using function.

It would take Quincy 16 x 3 = 48 mins to move all the small boxes and 5 x 10 = 50 mins to move all the large ones for a total of 98 mins.
It would take Celine 16 x 2 = 32 mins to move all the small boxes and 6 x 10 = 60 mins to move all the large ones for a total of 92 mins.
If you have Celine move all the small boxes while Quincy is working on the large ones he would be done with the small ones in 32 minutes.
He would be able to help move the big ones after that.
During this 32 mins, quincy would be done moving 6 big boxes and be 2 minutes into his 7th..
6 minutes later and celine is done with the 8th one, the 7th is finished and quincy is 3 mins into the 9th one. 6 mins later and celine is done with the 10th one and quincy has been sitting on his but for 4 minutes.
There is nothing that says that 2 people can move a single box faster than 1 so the total time used would be 32 + 6 + 6 =44 mins.

On the reverse, the soonest anyone could help the other would be 48 mins, so that does not work at all.

SO, they could be done at 9:44 AM

If we assume that two people can move a big one faster, then they could be done sooner..

Now, if we have Celine move all the small boxes but one, he could start helping Quincy move the large ones after 30 minutes.
Quincy would have just Finished his 6th box.
10 minutes later and quincy would have 2 more boxes and celine would only need 2 more minutes to finish the 10th.
so while celine finishes, quincy starts his 3 min tasl of moving the last small box.
they are done after 30+10+3 mins and celine has been resting for 1 minute.
43 mins means finishing at 9:43 am

The answer is C.

Now to put it simply

Celine moves 15 small boxes in 30 mins and 2 larges boxes in 12 minutes. He is done in 42 mins.
Quincy moves One small box in 3 minutes and 8 large boxes in 40 mins. He is done in 43 mins.
Both are done as a team in 43 mins.
start at 9:00 end at 9:43 AM
answer C

Or in math terms
Q=Quincy time in mins
C=Celine time in mins
T=Total time in mins to move all boxes and is the number we are searching for to add to the 9AM start time.
X = how many small boxes Celine moves
Y = How many big boxes Quincy Moves
R=(Q-C) and is the number of minutes one of the people will be sitting. (It could be a negative number)
Q=3(16-X)+5Y
C=6(10-Y)+2X
T=(Q+C)/2+R
T=Q+R
T=C-R
T=60-6Y+2X+R
T=48-3X+5Y-R
2T=108-X-Y
T=54-x/2-Y/2

I will let you figure the rest out. I am going to bed.

onQ QUINCY EYETOY BOXING PS2