2006 AMC 8 Problems/Problem 13
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[hide]Problem
Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time in the morning do they meet?
Solution 1
If Cassie leaves an hour earlier then Brian, when Brian starts, the distance between them will be . Every hour, they will get miles closer. , so 2 hours from AM is when they meet, which is .
Solution 2 (Basic Algebra)
Let be the # of hours after Cassie leaves, when both of them meet. In that hours, Cassie will travel miles. But, Brian will travel miles as he starts hours after Cassie. These two distances sum to the total distance of miles as they meet here, yielding the equation, . After distribution we get . After combining like terms and adding to both sides we get , and . So they meet hours after 8:30 a.m. which is .
- LearnForEver
Video Solution
https://youtu.be/EnpR7rjMYzg Soo, DRMS, NM
Video Solution by WhyMath
See Also
2006 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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 |
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