2005 CEMC Gauss (Grade 7) Problems/Problem 19
Problem
Chris and Pat are playing catch. Standing 
apart, Pat first throws the ball to Chris and then Chris throws the ball back to Pat. Next, standing 
apart, Pat throws to Chris and Chris throws back to Pat. After each pair of throws, Chris moves farther away from Pat.
They stop playing when one of them misses the ball. If the game ends when the 
throw is missed, how far apart are they standing and who misses catching the ball?
Solution
At each distance, two throws are made: the 
and 
throws are made at , the 
and 
are made at , and so on, with the 
and 
throws being made at 
.
Therefore, the throw is the first throw made at 
At each distance, the first throw is made by Pat to Chris, so Chris misses catching the throw at a distance of 
. The answer is therefore 
.
See Also
| 2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| CEMC Gauss (Grade 7) | ||
