2001 AMC 8 Problems/Problem 19: Difference between revisions
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==Solution== | ==Solution 1 == | ||
Since car N has twice the speed, it must be twice as high on the speed axis. Also, since cars M and N travel at the same distance but car N has twice the speed, car N must take half the time. Therefore, line N must be half the size of line M. Since the speeds are constant, both lines are horizontal. Reviewing the graphs, we see that the only one satisfying these conditions is graph <math> \boxed{\text{D}} </math>. | Since car N has twice the speed, it must be twice as high on the speed axis. Also, since cars M and N travel at the same distance but car N has twice the speed, car N must take half the time. Therefore, line N must be half the size of line M. Since the speeds are constant, both lines are horizontal. Reviewing the graphs, we see that the only one satisfying these conditions is graph <math> \boxed{\text{D}} </math>. | ||
==Solution 2 == | |||
Since Car N goes at a faster speed than Car M, it will take less time to get to the same destination. Reviewing the graphs, we see that only one graph fits this criteria, graph <math> \boxed{\text{D}} </math> | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2001|num-b=18|num-a=20}} | {{AMC8 box|year=2001|num-b=18|num-a=20}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 22:05, 13 August 2019
Problem
Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car M and Car N's speed and time are shown as solid line, which graph illustrates this?
![[asy] unitsize(12); draw((0,9)--(0,0)--(9,0)); label("time",(4.5,0),S); label("s",(0,7),W); label("p",(0,6),W); label("e",(0,5),W); label("e",(0,4),W); label("d",(0,3),W); label("(A)",(-1,9),NW); draw((0,4)--(4,4),dashed); label("M",(4,4),E); draw((0,8)--(4,8),linewidth(1)); label("N",(4,8),E); draw((15,9)--(15,0)--(24,0)); label("time",(19.5,0),S); label("s",(15,7),W); label("p",(15,6),W); label("e",(15,5),W); label("e",(15,4),W); label("d",(15,3),W); label("(B)",(14,9),NW); draw((15,4)--(19,4),dashed); label("M",(19,4),E); draw((15,8)--(23,8),linewidth(1)); label("N",(23,8),E); draw((30,9)--(30,0)--(39,0)); label("time",(34.5,0),S); label("s",(30,7),W); label("p",(30,6),W); label("e",(30,5),W); label("e",(30,4),W); label("d",(30,3),W); label("(C)",(29,9),NW); draw((30,4)--(34,4),dashed); label("M",(34,4),E); draw((30,2)--(34,2),linewidth(1)); label("N",(34,2),E); draw((0,-6)--(0,-15)--(9,-15)); label("time",(4.5,-15),S); label("s",(0,-8),W); label("p",(0,-9),W); label("e",(0,-10),W); label("e",(0,-11),W); label("d",(0,-12),W); label("(D)",(-1,-6),NW); draw((0,-11)--(4,-11),dashed); label("M",(4,-11),E); draw((0,-7)--(2,-7),linewidth(1)); label("N",(2,-7),E); draw((15,-6)--(15,-15)--(24,-15)); label("time",(19.5,-15),S); label("s",(15,-8),W); label("p",(15,-9),W); label("e",(15,-10),W); label("e",(15,-11),W); label("d",(15,-12),W); label("(E)",(14,-6),NW); draw((15,-11)--(19,-11),dashed); label("M",(19,-11),E); draw((15,-13)--(23,-13),linewidth(1)); label("N",(23,-13),E); [/asy]](http://latex.artofproblemsolving.com/c/f/5/cf5f4932472c29c9b113be5cbee4ee9eea008993.png)
Solution 1
Since car N has twice the speed, it must be twice as high on the speed axis. Also, since cars M and N travel at the same distance but car N has twice the speed, car N must take half the time. Therefore, line N must be half the size of line M. Since the speeds are constant, both lines are horizontal. Reviewing the graphs, we see that the only one satisfying these conditions is graph 
.
Solution 2
Since Car N goes at a faster speed than Car M, it will take less time to get to the same destination. Reviewing the graphs, we see that only one graph fits this criteria, graph
See Also
| 2001 AMC 8 (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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
