Difference between revisions of "1952 AHSME Problems/Problem 48"

(Created page with "== Problem == Two cyclists, <math>k</math> miles apart, and starting at the same time, would be together in <math>r</math> hours if they traveled in the same direction, but woul...")
 
(Solution)
Line 10: Line 10:
  
 
== Solution ==
 
== Solution ==
<math>\fbox{}</math>
+
<asy>
 +
pair A,B,C;
 +
A=(0,0); B=(8,0); C=(4,1);
 +
draw((A)--(B));
 +
label("$A$",A,S); label("$B$",B,SE); label("$k$",C,SW);
 +
</asy>
  
 
== See also ==
 
== See also ==

Revision as of 19:46, 20 April 2020

Problem

Two cyclists, $k$ miles apart, and starting at the same time, would be together in $r$ hours if they traveled in the same direction, but would pass each other in $t$ hours if they traveled in opposite directions. The ratio of the speed of the faster cyclist to that of the slower is:

$\text{(A) } \frac {r + t}{r - t} \qquad \text{(B) } \frac {r}{r - t} \qquad \text{(C) } \frac {r + t}{r} \qquad \text{(D) } \frac{r}{t}\qquad \text{(E) } \frac{r+k}{t-k}$

Solution

[asy] pair A,B,C; A=(0,0); B=(8,0); C=(4,1); draw((A)--(B)); label("$A$",A,S); label("$B$",B,SE); label("$k$",C,SW); [/asy]

See also

1952 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 47
Followed by
Problem 49
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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png