 #2 90. THE FRIENDLY FOOTRACE  |
 Glen and Jeff decided to run a race over a distance of 100 metres.
“Tell you what,” said Jeff. “We’ll run it again, and I’ll take a handicap. I’ll start three metres behind the starting line.” “That sounds fair,” agreed Glen. If the competitors run the second race at the same speeds as the first race, what will the outcome be?
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Hints and strategies |
| HINT 1
Here is a cryptic hint: translation. |
| HINT 2
Think about the second race. What is the state of play when Glen reaches the 97 metre mark? |
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SOLUTION
Jeff wins again. The runners are abreast when Glen reaches the 97 metre mark. After that, Jeff, who is the faster runner, moves ahead. |
| EXTENSIONS This problem has a very simple solution which we have given, but it look like one of those time – distance problems. Assuming that Jeff runs at 100 m/minute (very slow!) and Glen runs at 97 m/minute, calculate how long it takes Jeff to run 193 metres, and Glen to run 100 metres. Does this confirm our earlier answer? And which way did you solve this problem?! |
The result was close, but Jeff won by three metres. That is, when Jeff had run 100 metres, Glen had only completed 97 metres.