Hints and solutions to Draw a Picture #2
Billy, Ray, Gary, Clayton, Floyd and Pete just completed a 3000 meter
race. Use these clues to help you determine the order in which they
finished.
- Floyd finished 10 seconds behind Gary.
- Ray beat Pete by 20
seconds.
- Billy finished 4 seconds behind Gary and 30 seconds ahead of
Ray.
- Clayton's finish was halfway between Floyd and Pete.
-
To solve this problem, we make a diagram to show how the racers finished.
Using one of the clues at a tile, we can construct the following diagram:
To draw the diagram, plot each piece of information. First, Gary beats
Floyd by
10 seconds, and also Gary beats Billy by 4 seconds. Since Billy beats Ray
by 30 seconds,
Ray is a total of 34 seconds behind Gary. And Pete is 20 seconds behind
Ray, and
so Pete is 54 seconds behind Gary. Finally, Clayton is halfway between
Floyd
and Pete. Since Floyd is 10 seconds behind Gary and Pete is 54 seconds
behind Gary,
there are 44 seconds between Floyd and Pete. So Floyd beats Clayton by 22
seconds
and Clayton beats Pete by 22 seconds. And we then know that Clayton is 32
seconds
behind Gary. Thus, the order of finish is:
- Gary (winner)
- Billy (4 sec behind Gary)
- Floyd (10 sec behind Gary)
- Clayton (32 sec behind Gary)
- Ray (34 sec behind Gary)
- Pete (54 sec behind Gary)
