Difference between revisions of "1992 AJHSME Problems/Problem 19"
Redjack-512 (talk | contribs) m (→Problem) |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | The distance between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits on an interstate highway is <math>118</math> miles. If any two exits are at least <math>5</math> miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits? | + | The distance between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits on an interstate highway is <math>118</math> miles. If any two consecutive exits are at least <math>5</math> miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits? |
<math>\text{(A)}\ 8 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 47 \qquad \text{(E)}\ 98</math> | <math>\text{(A)}\ 8 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 47 \qquad \text{(E)}\ 98</math> | ||
Latest revision as of 22:26, 25 May 2021
Problem
The distance between the 
and 
exits on an interstate highway is 
miles. If any two consecutive exits are at least 
miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the and exits?
Solution
There are 
pairs of consecutive exits. To find the maximum number of miles of one of these, the other 
must be equal to the minimum number yielding a total of 
miles. The longest distance must be 
.
See Also
| 1992 AJHSME (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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
