2017 AMC 10A Problems/Problem 9
Contents
Problem
Minnie rides on a flat road at kilometers per hour (kph), downhill at
kph, and uphill at
kph. Penny rides on a flat road at
kph, downhill at
kph, and uphill at
kph. Minnie goes from town
to town
, a distance of
km all uphill, then from town
to town
, a distance of
km all downhill, and then back to town
, a distance of
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
-km ride than it takes Penny?
Solution
The distance from town to town
is
km uphill, and since Minnie rides uphill at a speed of
kph, it will take her
hours. Next, she will ride from town
to town
, a distance of
km all downhill. Since Minnie rides downhill at a speed of
kph, it will take her half an hour. Finally, she rides from town
back to town
, a flat distance of
km. Minnie rides on a flat road at
kph, so this will take her
hour. Her entire trip takes her
hours.
Secondly, Penny will go from town
to town
, a flat distance of
km. Since Penny rides on a flat road at
kph, it will take her
of an hour. Next Penny will go from town
to town
, which is uphill for Penny. Since Penny rides at a speed of
kph uphill, and town
and
are
km apart, it will take her
hours. Finally, Penny goes from Town
back to town
, a distance of
km downhill. Since Penny rides downhill at
kph, it will only take her
of an hour. In total, it takes her
hours, which simplifies to
hours and
minutes.
Finally, Penny's
Hour
Minute trip was
minutes less than Minnie's
Hour
Minute Trip
Review:
Video Solution
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 |
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