Difference between revisions of "2002 AMC 8 Problems/Problem 18"
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==Solution 2== | ==Solution 2== | ||
For the first five days, each day you are <math>10</math> minutes short of <math>85</math> minutes. And for the next three days, you are <math>5</math> minutes above <math>85</math> minutes. So in total you are missing <math>3*5-5*10</math>, which equals to negative <math>35</math>. So on the ninth day, to have an average of <math>85</math> minutes, Gage need to skate for <math>85+35</math> minutes, which is <math>120</math> minutes, or <math>\boxed{\text{(E)}\ 2\ \text{hr}}</math>. | For the first five days, each day you are <math>10</math> minutes short of <math>85</math> minutes. And for the next three days, you are <math>5</math> minutes above <math>85</math> minutes. So in total you are missing <math>3*5-5*10</math>, which equals to negative <math>35</math>. So on the ninth day, to have an average of <math>85</math> minutes, Gage need to skate for <math>85+35</math> minutes, which is <math>120</math> minutes, or <math>\boxed{\text{(E)}\ 2\ \text{hr}}</math>. | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://www.youtube.com/watch?v=Ea1C64_qBH4 | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2002|num-b=17|num-a=19}} | {{AMC8 box|year=2002|num-b=17|num-a=19}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 20:54, 20 December 2022
Problem
Gage skated hr
min each day for
days and
hr
min each day for
days. How long would he have to skate the ninth day in order to average
minutes of skating each day for the entire time?
Solution 1
Converting into minutes and adding, we get that she skated minutes total, where
is the amount she skated on day
. Dividing by
to get the average, we get
. Solving for
,
Now we convert back into hours and minutes to get
.
Solution 2
For the first five days, each day you are minutes short of
minutes. And for the next three days, you are
minutes above
minutes. So in total you are missing
, which equals to negative
. So on the ninth day, to have an average of
minutes, Gage need to skate for
minutes, which is
minutes, or
.
Video Solution
https://www.youtube.com/watch?v=Ea1C64_qBH4
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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.