Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2017 AMC 10A Problems/Problem 9

Revision as of 17:50, 8 February 2017 by Ishankhare (talk | contribs) (→‎Problem)

Problem

Minnie rides on a flat road at $20$ kilometers per hour (kph), downhill at $30$ kph, and uphill at $5$ kph. Penny rides on a flat road at $30$ kph, downhill at $40$ kph, and uphill at $10$ kph. Minnie goes from town $A$ to town $B$, a distance of $10$ km all uphill, then from town $B$ to town $C$, a distance of $10$ km all uphill, then from town $B$ to town $C$, a distance of $15$ km all downhill, and then back to town $A$, a distance of $20$ km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the $45$-km ride than it takes Penny?

$\textbf{(A)}\ 45\qquad\textbf{(B)}\ 60\qquad\textbf{(C)}\ 65\qquad\textbf{(D)}\ 90\qquad\textbf{(E)}\ 95$

Solution

The distance from town A to town B is 10km uphill, and since Minnie rides uphill at a speed of 5 kph, it will take her 2 hour. Next, she will ride from town B to town C, a distance of 15 km all downhill. Since Minnie rides downhill at a speed of 30 kph, it will take her half(.5) of an hour. Finally, she rides from town c back to town a, a flat distance of 20 km. Minnie rides on a flat road at 20 kph, so this will take her 1 hour. Her entire trip takes her 3.5 hours. Secondly, Penny will go from town A to town C, a flat distance of 20km. Since penny rides on a flat road at 30 kph, it will take her two thirds(2/3) of an hour. Next Penny will go from town C to town B, which is uphill for Penny. Since penny rides at a speed of 10kph uphill, and town C and B are 15 km apart, it will take her one and a half(1.5) hours. Finally, Penny goes from Town B back to town A, a distance of 10km downhill. Since Penny rides downhill at 40 kph, it will only take her a quarter of an hour. In total, it takes her 29/12 hours, which simplifies to 2 hours and 25 minutes. Finally, Penny's 2 Hour 25 Minute trip was 65 minutes less than Minnie's 3 Hour 30 Minute Trip

See Also

2017 AMC 10A (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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 AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10A_Problems/Problem_9&oldid=83058"