Minus' Solution to

Hey, I'm on time!
Posted Weeks of October 20 - Novmeber 1, 1997

Lunch is 270 minutes away.
Sally arrives at the picnic site after (5/6)(270) = 225 minutes Which means she arrives at 11:45 a.m.
Billy arrives there after (6/5)(270) = 324 minutes So he arrives at 1:24 p.m.

A little simple subtraction and we discover that Sally and Billy arrive 99 minutes apart. Boy, was Billy in hot water, or what?

Your Solutions

Gena Covington, Paul Harrell, Matthew Stone, Jordan Thorndyke, and Jack Ulrich, from South Scotland School in Laurinburg, NC, whipped-up this main course wonder with some flair. Thanks for easing Minus' mind. All this time, he thought his challenges were just torturing you all.

We worked on this problem in our Fourth Grade Class in groups, and we came up with this solution:

From 8:00 AM to 12:30 PM there are four and one-half hours.  There are 12 five-minute segments in one hour and 10 six-minute segments in one hour. You would take the 4 and 1/2 hours and the 12 five-minute segments and multiply them to get 54 minutes.  Then you would take the 10 six-minute segments and multiply them by 4 and 1/2 hours to get 45 minutes.  Then you would add the 45 minutes and the 54 minutes to discover that Sally and Billy arrived 99 minutes apart. 

We had fun discovering the answer. 

Jessi Barnes and Julie Gunter, two fifth grade students at South Scotland Elementary in Laurinburg, NC, offered Minus this chow-down-now dish. It was a bit crispy in parts, but that's how sharks like their food--CRUNCHY
We went the long way around, but came up with this way of solving the problem.

We knew that the 4 and 1/2 hours between 8:00 and 12:30 were actually 270 minutes. So we set up a pattern of working out the actual minutes that had passed and the minutes that had passed on Billy's and Sally's watches.

Billy's watch went up 5 minutes while the actual time went up 6 minutes. When the actual time was at 270 minutes, Billy's watch read only 225 minutes.  When his watch finally read 270 minutes the actual time read 324 minutes, or 5 hours and 24 minutes.  Billy was 54 minutes late.  To figure Sally's arrival time we just looked at it backwards:  When the actual time read 225  minutes, Sally's watch read 270 minutes, or 3 hours and 45 minutes.  Sally was 45 minutes too early.  So Sally and Billy were actually 99 minutes apart.

We don't think they got to eat lunch together!

Tricia Kao, A.K.A. peeshy, worked out this solution using "lots" of time. Okay, it's an awful pun, but Minus has to keep you all entertained somehow. We noticed that peeshy had Billy arriving before Sally. Hmm...this could lead into a dangerous debate. Do women arrive late more often than men? Or, vice versa?
Here's my working:
lots of 5 min   lots of 6 min
8-9 = 1 hr 12 10
8-10 = 2 hr 24 20
8-11 = 3 hr 36 30
8-12 = 4 hr 48 40
8-12:30 = 4 hr, 30 min 54 45

Billy: In 4 hr 30 min, there are 45 lots of 6 minutes therefore, each lot of 6 will become 5. 45 x 5 = 225 minutes = 3 hours 45 minutes so arriving at 11:45am.
Sally: In 4 hr 30 min, there are 54 lots of 5 minutes. Therefore, each lot of 5 wil become 6. 54 x 6 = 324 minutes
324 minutes = 5 hours 24 minutes, Arriving at 1:24pm.

11:45 - 12:45 = 1hr
11:45 - 1:45 = 2hr
11:45 - 1:24 = 1hr 39 minutes.
1 hour 39 minutes = 60 + 39 minutes

Billy and Sally arrive 99 minutes apart for the picnic.

Minus' longtime Aussie buddies, Taryn Chua and Eden Ridgeway, of MLC in Australia (Year Nine and 3/4), always cook-up dishes to keep him fit as a fiddle. They also love teasing our feisty friend. Wait until Minus' girlfriend finds out...
Here is our solution:

12:30 minus 8:00 = 4.5hrs
For Sally, we must add twelve minutes for every hour. 4.5hrs times 12 = 54, so Sally is 54 minutes early. For Billy, we must add ten minutes for every hour. 4.5hrs times 10 =45, so Billy is 45 minutes late.

This means that they arrive 99 minutes apart (1 hour and 39 minutes).
Bye, bye!

Oritt Levi [rattyritty@rocketmail.com] offered this tasty solution at the last minute. The extra cooking time for this dish was well worth it, because Oritt shows us an efficient way to work with this week's ingredients.
To: Minus@actden.com

Hey, I'm on time . . . . . . sorry if I'm late!!!

We have 270 mins.

How many 6 mins are there that Billy counts 5 mins for? = 45. and 45 x 5 = 225.  So for every 270 mins, Billy counts 225 mins, so he arrives at 11:45AM

How many 5 mins are there that Sally counts 6 mins for? = 54.  And 54 x 6 = 324.  So for every 270 mins, Sally counts 324 mins.  So she arrives at 1:24PM

How many mins between 11:45AM and 1:24PM? =99

Will Meyers also has Billy arriving before Sally. Wait a second...if Billy's watch is running slow, how can he be early? Fox Mulder, on The X-Files, would probably say, "It was an alien abduction."
Since Billy's watch runs slow and there are 45 - 6 minute intervals between 8:00 a.m. and 12:30 p.m. he will arrive 45 minutes early at 11:45 a.m.

Since Sally's watch runs fast abd there are 54 - 6 minute intervals between 8:00 a.m. and 12:30 p.m. she will arrive 54 minutes late at 1:24 p.m.

This means they  will be 45 minutes + 54 minute = 99 minute or 1 hour 39 minutes apart.

We will have to hope Billy is not in a hurry to get some place else or he may miss Sally.

A mysterious chef at [VAgarwala@aol.com] sent this healthy offering to Minus. All the right ingredients are there, but who are you?
Both Bill and Sally are "measuring" 270 minutes on their watches (8:00 A.M. to 12:30 P.M.)

Every 5 minutes on Bill's watch are actually 6 minutes. Therefore, 270 minutes on Bill's watch are actually (6/5)x270 = 324 minutes

Every 6 minutes on Sally's watch are actually 5 minutes. Therefore, 270 minutes on Sally's watch are actually (5/6)x270 = 225 minutes

Therefore, they come  (324 - 225) = 99 minutes apart.

Kevin Veenstra and Fernando Soler offered Minus two extra dashes of seasoning for this week's meal. "Hey, can you pass the salt while you're at it?"
99 minutes

Thanks for all your tasty treats.
It's time to tuck Minus into bed.
He gets awful sleepy after a big meal.