Difference between revisions of "1999 AMC 8 Problems/Problem 4"
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| − | ==Problem | + | ==Problem== |
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn? | The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn? | ||
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After 4 hours, we see that Bjorn biked 45 miles, and Alberto biked 60. Thus the answer is <math>60-45=15</math> <math>\boxed{\text{(A)}}</math>. | After 4 hours, we see that Bjorn biked 45 miles, and Alberto biked 60. Thus the answer is <math>60-45=15</math> <math>\boxed{\text{(A)}}</math>. | ||
| + | ==Solution 2== | ||
| + | We see that each dot is <math>15</math> units away from the nearest one above it. So the answer is <math>\boxed{\text{A}} </math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=1999|num-b=3|num-a=5}} | {{AMC8 box|year=1999|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 21:02, 14 April 2017
Contents
Problem
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn?
![[asy] for (int a = 0; a < 6; ++a) { for (int b = 0; b < 6; ++b) { dot((4*a,3*b)); } } draw((0,0)--(20,0)--(20,15)--(0,15)--cycle); draw((0,0)--(16,12)); draw((0,0)--(16,9)); label(rotate(30)*"Bjorn",(12,6.75),SE); label(rotate(37)*"Alberto",(11,8.25),NW); label("$0$",(0,0),S); label("$1$",(4,0),S); label("$2$",(8,0),S); label("$3$",(12,0),S); label("$4$",(16,0),S); label("$5$",(20,0),S); label("$0$",(0,0),W); label("$15$",(0,3),W); label("$30$",(0,6),W); label("$45$",(0,9),W); label("$60$",(0,12),W); label("$75$",(0,15),W); label("H",(6,-2),S); label("O",(8,-2),S); label("U",(10,-2),S); label("R",(12,-2),S); label("S",(14,-2),S); label("M",(-4,11),N); label("I",(-4,9),N); label("L",(-4,7),N); label("E",(-4,5),N); label("S",(-4,3),N); [/asy]](http://latex.artofproblemsolving.com/0/7/b/07bfc35302b906872d0fbe29df5e4d23b2a658d9.png)
Solution
After 4 hours, we see that Bjorn biked 45 miles, and Alberto biked 60. Thus the answer is 
.
Solution 2
We see that each dot is 
units away from the nearest one above it. So the answer is 
.
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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. 
