Minus' Solution to

Soccer Slackers' Sentence
Posted February 24 - March 2, 1997

Ely has to catch up to Luke, so whatever distance Luke runs, Ely has to run 480 meters more.

Luke has to travel x kilometers, and Ely has to travel (x + 0.480) kilometers.

Luke has travelled 960 meters = 0.96 km, and Ely has traveled 960 + 480 meters = 1.44 km. In order to have travelled 960 meters, Luke is back at point A, and that is where Ely and Luke meet.

In order to run 960 meters, Luke takes 0.12 hours = 7.2 minutes, which is 7 minutes and 12 seconds, so it is 12:07:12 when they meet.

Your Solutions

Lauren Deer, of Robert Smalls Middle School in Beaufort, SC, devised this clever solution for Minus to munch on. Boy, was our fickle shark pleased with this treat!

The answer is 12:07 and 12 seconds and they will run into each other at point A.

Ely is 480 meters behind Luke. Let x = the time. Luke runs at a rate of 8,000 m/hr. So, Luke's distance is 8,000 m/hrs. (x hrs)+ 480 m.
Ely runs at a rate of 12,000 m/hr.
So, Ely's distance is 12,000 m/hr. (x hrs).
This is the equation: 8,000 m(hrs. ) + 480 m = 12,000 m (x hrs.)

To solve the equation, first subtract 8,000 m (x hrs.) from each side and you get 480 m = 4,000 m (x hrs.). Next you divide each side by 4,000 m and get x = .12 hrs. or 7 minutes and 12 sec. Then you add 7 minutes and 12 sec. to 12:00 to find the time they ran.

To find where they meet, substitute the time for x to find the distance for each boy who ran.
For Luke, (8,000 m/hr.)(.12 hrs) = 960 m which is one time around. For Ely, (12,000 m/hr.(.12) hrs. = 1440 m. This distance is to 1 and 1/2 times around which will be the same point Luke will be at this time, which will be point A.

Herman Steiniger, also of Robert Smalls Middle School, found a different way of coming up with the right answer. Looks like Herman really knows how to manipulate those fractions!

First, I converted all the meters to kilometers. Next, I found out how far Luke and Ely can run in a minute, Luke runs 2/15 of a kilometer in a minute and Ely can run 1/5 of a kilometer per minute which is faster than Luke. Since Luke has a 12/25 km head start the following equation can be used to find out the number of minutes it will take Ely to catch up with Luke.
Let x = the time.
12/25 + 2/15x = 1/5x

The solution to the equation is 7 and 1/5 minutes or 7 minutes 12 seconds.

If Luke can run at a rate of 2/15 km per minute, he will run .96 km in 7 and 1/5 minutes which is 1 lap and end up at point A. If Ely is running at a rate of 1/5 km per minute, he will run 1.44 km in 7 and 1/5 minutes and meet Luke at point A at 12:07 and 12 seconds.

A big, heart-felt, shark thanks
goes to Patricia G. Fields, and her
two math wizards, for submitting
this week's delicious solutions!