Minus' Solution to

Dance the Night Away
Posted Jan 27 - Feb 2, 1997

First dancing partner: 7:02 p.m. - 7:05:30 p.m.
Second dancing partner: 7:05:30 p.m. - 7:08 p.m.
. . . 7:02 p.m. + [105(2.5) - 2.5] minutes = 7:02 p.m. + 260 minutes =
7:02 p.m. + 4 hours + 20 minutes = 11:22 p.m.

Now to be honest, Minus had to accept what Mr. T. and his Little Einsteins in Texas had to say. Mr. T. wrote:

The question asked, "At what time will the Prince be dancing with maiden #105." He will "begin" dancing with 105 at 11:22, but he will "be" dancing with her from 11:22 until 11:24 and 30 seconds. (We go to great lengths in my class to answer the exact question being asked and answer it thoroughly. We trust you expect the same!)

Minus was not as careful as the wily Texans when he invented this question, and was indeed thinking of just the start time.

Nevertheless, Prince Charming will be pretty busy if he wants to dance with every girl!

Given all the hoopla above, it is hardly surprising that Mr. T. and his Little Einsteins in Texas came up with this week's finest entree. Our resident math shark couldn't be more grateful...

If the Prince started dancing at 7:02 PM with maiden #1, then after the first 2.5 minutes he would begin with maiden #2. Therefore, to calculate the starting time with maiden #105, you must subtract 1 from 105 = 104 to account for the first maiden at time zero. So, 105 - 1 = 104; (104)(2.5) = 260 minutes = 4 hours and 20 minutes.
7:02 + 4 hours, 20 minutes = 11:22 PM (When the Prince starts dancing with maiden #105)

When I first started I made a chart numbering 1 - 105 and I put the time next to the number and the numbers stood for the dancing partners. Then I started adding 2.5's, but I got bored so I started adding 5's because 2.5 + 2.5 =5. Then I thought it was taking so long. So, I started adding 10 because 5 + 5 = 10 and then I ended up with 11:22 P.M. This is when he danced with his 105th dance partner.

When you do this problem, you have to multiply 2.5 x 104. This will give you the number of minutes it took to dance with 104 people (260 minutes). This is also when he starts dancing with his 105th partner. You divide 260 by 60 to give you how many hours this took ( 4 hours, 20 minutes). You then add this number to 7:02 and you get 11:22 PM.

If the prince changes partners every two and a half minutes, and you want to find out when he is dancing with the 105th partner, then you multiply 104 * 2.5 because if you multiplied it by 105 then you would be calculating when the prince moves on to the 106th partner. Anyways, that comes out to be 260. Then you must divide it by 60 because it is in minutes and you need it in hours. You end up getting 4.333333... or 4 1/3. You change the 1/3 into minutes which is 20 and you add 4 hours and 20 minutes to 7:02.
The answer is 11:22 PM.

The prince will be dancing with his 105th partner at 11:22 pm.
If the prince takes his first partner at 7:02 pm, 104 dances later he will take his 105th partner.

104 x 2.5 = 260 minutes
260 / 60 = 4 hours and 20 minutes
7:02 + 4:20 = 11:22 PM