1968 AHSME Problems/Problem 25
Contents
Problem
Ace runs with constant speed and Flash runs 
times as fast, 
. Flash gives Ace a head start of 
yards, and, at a given signal, they start off in the same direction. Then the number of yards Flash must run to catch Ace is:
Solution
Solution 2
Let 
denotes the distance Ace needs to run after the yard. Since the distance they run with same amount of time is proportional to their speed, we have
![\[\frac{1}{x}=\frac{k}{y+k}\]](http://latex.artofproblemsolving.com/6/7/6/676fb9755840e3d663be39211115de1e4fba112d.png)
![\[k=\frac{y}{x-1}\]](http://latex.artofproblemsolving.com/4/6/5/46559ef09e4144af8a696534779640a7eecb03eb.png)
Thus the total distance ran by Flash is
![\[y+k=y+\frac{y}{x-1}=\frac{xy}{x-1}\boxed{C}\]](http://latex.artofproblemsolving.com/9/8/b/98be3a53ebcf5a85a21c0107c18d09b694651022.png)
~ Nafer
See also
| 1968 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Problem 26 | |
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