Difference between revisions of "2018 AMC 8 Problems/Problem 6"
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| − | Since Anh drives <math>3</math> times as fast on the highway, it takes him <math>\frac{1}{3}</math> of the time to drive <math>10</math> miles on the highway than on the coastal road. <math>\frac{1}{3}</math> of <math>30</math> is <math>10</math>, and since he drives <math>50</math> miles on the highway, we multiply <math>10</math> by <math>5</math> to get <math>50</math>. This means it took him <math>50</math> minutes to drive on the highway, and if we add the <math>30</math> minutes it took for him to drive on the coastal road, we would get <math>80</math>. | + | Since Anh drives <math>3</math> times as fast on the highway, it takes him <math>\frac{1}{3}</math> of the time to drive <math>10</math> miles on the highway than on the coastal road. <math>\frac{1}{3}</math> of <math>30</math> is <math>10</math>, and since he drives <math>50</math> miles on the highway, we multiply <math>10</math> by <math>5</math> to get <math>50</math>. This means it took him <math>50</math> minutes to drive on the highway, and if we add the <math>30</math> minutes it took for him to drive on the coastal road, we would get <math>\boxed{\textbf{(C) }80}</math>. |
-UnstoppableGoddess | -UnstoppableGoddess | ||
Revision as of 12:22, 5 January 2022
Contents
Problem
On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?
Solution 1
Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is 
mph. His speed on the highway then is 
mph. He drives 
miles, so he drives for 
hours, which is equal to minutes (Note that miles per hour is the same as 
mile per minute). The total amount of minutes spent on his trip is 
Solution 2
Since Anh drives 
times as fast on the highway, it takes him 
of the time to drive 
miles on the highway than on the coastal road. of 
is , and since he drives miles on the highway, we multiply by 
to get . This means it took him minutes to drive on the highway, and if we add the minutes it took for him to drive on the coastal road, we would get 
.
-UnstoppableGoddess (helped by qkddud)
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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. 
